This dissertation consists of three studies of immersed finite element (IFE) methods for inter- face problems related to partial differential equations (PDEs) with discontinuous coefficients. These three topics together form a continuation of the research in IFE method including the extension to elasticity systems, new breakthroughs to higher degree IFE methods, and its application to inverse problems. First, we extend the current construction and analysis approach of IFE methods in the literature for scalar elliptic equations to elasticity systems in the vector format. In particular, we construct a group of low-degree IFE functions formed by linear, bilinear, and rotated Q1 polynomials to weakly satisfy the jump conditions of elasticity interface problems. Then we analyze the trace inequalities of these IFE functions and the approximation capabilities of the resulted IFE spaces. Based on these preparations, we develop a partially penalized IFE (PPIFE) scheme and prove its optimal convergence rates. Secondly, we discuss the limitations of the current approaches of IFE methods when we try to extend them to higher degree IFE methods. Then we develop a new framework to construct and analyze arbitrary p-th degree IFE methods. In this framework, each IFE function is the extension of a p-th degree polynomial from one subelement to the whole interface element by solving a local Cauchy problem on interface elements in which the jump conditions across the interface are employed as the boundary conditions. All the components in the analysis, including existence of IFE functions, the optimal approximation capabilities and the trace inequalities, are all reduced to key properties of the related discrete extension operator. We employ these results to show the optimal convergence of a discontinuous Galerkin IFE (DGIFE) method. In the last part, we apply the linear IFE methods in the literature together with the shape optimization technique to solve a group of interface inverse problems. In this algorithm, both the governing PDEs and the objective functional for interface inverse problems are discretized optimally by the IFE method regardless of the location of the interface in a chosen mesh. We derive the formulas for the gradients of the objective function in the optimization problem which can be implemented efficiently in the IFE framework through a discrete adjoint method. We demonstrate the properties of the proposed algorithm by applying it to three representative applications. / Doctor of Philosophy / Interface problems arise from many science and engineering applications modeling the transmission of some physical quantities between multiple materials. Mathematically, these multiple materials in general are modeled by partial differential equations (PDEs) with discontinuous parameters, which poses challenges to developing efficient and reliable numerical methods and the related theoretical error analysis. The main contributions of this dissertation is on the development of a special finite element method, the so called immersed finite element (IFE) method, to solve the interface problems on a mesh independent of the interface geometry which can be advantageous especially when the interface is moving. Specifically, this dissertation consists of three projects of IFE methods: elasticity interface problems, higher-order IFE methods and interface inverse problems, including their design, analysis, and application.

This study analyses the causes of error in the written english of black senior secondary pupils and teacher trainees. Using Error Analysis and Contrastive Analysis in a form known as Interference Analysis and covering a full range of grammatical, syntactical and lexical issues! erroneous items in English are compared with the same items in the learners' first language in order to isolate an identify such errors. Analysis of these errors shows which are due to direct interlingual transfer which are not completely attributable to direct transfer, and which are intralingual, the result of idiosyncratic language usage or merely mistakes rather than errors. While recognizing the degree to which Black learners' language habits have become fossilized and the extent to which standerdized errors form part of the English used by Bantu-speaking students, this study sets out to improve proficiency in English by explaining the the causes of error and by suggesting possible remedial approaches. / English Studies / M.A. (English)

This study investigated common English language errors made by Oshiwambo, Afrikaans and Silozi First Language speakers. The study examined errors in a corpus of 360 essays written by 180 participants. Errors were identified and classified into various categories. The four most common errors committed by the participants were tenses, prepositions, articles and spelling. The study is important to educators and study material developers who should become aware of the kind of errors that their target learners make, so that they are in a better position to put appropriate intervention strategies into place. For learners, error analysis is important as it shows the areas of difficulty in their writing. The limitations and some pedagogical implications for future study are included at the end of this research paper. / English Studies / M. A. (TESOL)

published_or_final_version / Language Studies / Master / Master of Arts

Cette recherche pseudo-longitudinale privilégiant une approche sociolinguistique et didactique s’inscrit dans le domaine du développement de l’interlangue à travers l’analyse des erreurs morphosyntaxiques du français. Notre public s’est compose des lycéens kenyans anglophones. Cela a été effectué au sein de la capitale du Kenya, Nairobi et de sa banlieue. Les entretiens sur le terrain comprenant des exercices descriptifs et conversationnels à l’oral et à l’écrit, ont mené à la description, l’analyse et l’étiologie des erreurs morphosyntaxiques en français langue étrangère (désormais FLE) dans les productions des apprenants dans un contexte lycéen. L’analyse de ce corpus écrit et oral a révélé les erreurs morphosyntaxiques écrites et orales en français les plus récurrentes ainsi que leurs causes chez les lycéens kenyans. Ce travail s’achève par l’élaboration de propositions didactiques à l’écrit et à l’oral présentant des pistes de réflexion sur la remédiation des erreurs morphosyntaxiques des lycéens kenyans. / This research favoring a sociolinguistic and didactic approach is based on the development of interlanguage through the analysis of morphosyntactical errors in French by English speaking Kenyan high school students in Nairobi and its suburbs. Field research composed of descriptive and conversational oral and written exercises in French as a foreign language was carried out on selected high school students. This paved way to the description and analysis of morphosyntactical errors in French. The analysis of the written and oral corpus helped to identify the most recurrent morphosyntactical and written errors in French, as well as their etiology. This pseudo-longitudinal research culminated in suggested written and oral didactical activities aimed at the correction of these morphosyntactical errors.

Apesar de o Brasil ser o país com a maior comunidade japonesa fora do Japão, ainda há poucos estudos sobre a aquisição e aprendizagem do português por falantes japoneses. Partindo da descrição do sistema silábico da língua portuguesa (CÂMARA JR., 1970; FERREIRA NETTO, 2001; CRISTÓFARO SILVA, 2009; CAGLIARI, 2007; CAVALIERE, 2005) e da língua japonesa (SHIBATANI, 1987; ITÔ, 1986; McCAWLEY, 1968; HINDS, 1986), pretende-se observar por meio da Análise de Erros (CORDER, 1967) quais as estratégias utilizadas por falantes japoneses em processo de aprendizagem da língua portuguesa para pronunciar duas estruturas silábicas que não existem em sua língua materna: sílabas CVC terminadas em /r/ ou /s/, e sílabas com mais de uma consoante pré-vocálica do tipo CCV, com /r/ ou /l/ ocupando a segunda posição de ataque. A partir dessa observação, busca-se determinar quais dessas estruturas representam maior dificuldade para o aprendiz japonês. Para a composição do corpus, foram criados dezenove nomes fictícios com as estruturas silábicas em questão e sete informantes foram gravados. Ainda que não tenha sido uma pesquisa quantitativa, por meio da comparação dos resultados foi possível verificar a maior facilidade de produzir sílabas CVC em relação às CCV e, para a maioria, o número de acertos foi maior com a consoante /s/ em posição de coda e /r/ na segunda posição de ataque complexo. Quanto à estratégia utilizada, o uso de inserção vocálica foi maior que o de apagamento, exceto quando /r/ ocupa a posição de coda. A pesquisa mostrou que a dificuldade maior ou menor do aprendiz pode ser entendida a partir de processos fonológicos que acontecem na L1, no caso a língua japonesa. / Although Brazil is the country with the largest Japanese community outside Japan, there are few studies about Portuguese acquisition and learning by Japanese speakers. Based on the description of the syllabic system of the Portuguese language (CÂMARA JR., 1970; FERREIRA NETTO, 2001; CRISTÓFARO SILVA, 2009; CAGLIARI, 2007; CAVALIERE, 2005) and of the Japanese language (SHIBATANI, 1987; ITÔ, 1986; McCAWLEY, 1968; HINDS, 1986), we intend to observe through Error Analysis (CORDER, 1967) the strategies used by Japanese learners of Portuguese to pronounce two syllable structures that do not exist in their native language: CVC syllables closed by /r/ or /s/ and CCV syllables with /r/ or /l/ in the second onset position. From this observation, we seek to determine which of these structures represents more difficulty for Japanese learners. To compose the corpus, nineteen fictitious names with the syllabic structure in question were created and seven informants were recorded. Although it has not been a quantitative research, by comparing the results we could verify that it was easier to produce CVC syllables than CCV ones. In addition, for most of the informants, the number of correct production was higher with the consonant /s/ in coda position and /r/ in the second onset position. For the strategy used, the use of vowel insertion was higher than deletion, except when /r/ occupies the coda position. Research has shown that the greater or lesser difficulty of the learner can be understood from phonological processes that occur in L1, in this case the Japanese language.

La modélisation et la simulation numérique des interfaces sont au coeur de nombreuses applications en mécanique des fluides et des solides, telles que la biologie cellulaire (déformation des globules rouges dans le sang), l'ingénierie pétrolière et la sismique (modélisation de réservoirs, présence de failles, propagation des ondes), l'aérospatiale (problème de rupture, de chocs) ou encore le génie civil. Cette thèse porte sur l'approximation des problèmes d'interface et d'interphase en mécanique des fluides par la méthode NXFEM, qui permet de prendre en compte de façon précise une discontinuité non alignée avec le maillage. Nous nous sommes d'abord intéressés au développement de la méthode NXFEM pour des éléments finis non-conformes pour prendre en compte une interface séparant deux milieux. Nous avons proposé deux approches pour les équations de Darcy et de Stokes. La première consiste à modifier les fonctions de base de Crouzeix-Raviart sur les cellules coupées et la deuxième consiste à rajouter des termes de stabilisation sur les arêtes coupées. Les résultats théoriques obtenus ont été ensuite validés numériquement. Par la suite, nous avons étudié la modélisation asymptotique et l'approximation numérique des problèmes d'interphase, faisant apparaître une couche mince. Nous avons considéré d'abord les équations de Darcy en présence d'une faille et, en passant à la limite dans la formulation faible, nous avons obtenu un modèle asymptotique où la faille est décrite par une interface, avec des conditions de transmission adéquates. Pour ce problème limite, nous avons développé une méthode numérique basée sur NXFEM avec éléments finis conformes, consistante et stable. Des tests numériques, incluant une comparaison avec la littérature, ont été réalisés. La modélisation asymptotique a été étendue aux équations de Stokes, pour lesquelles nous avons justifié le modèle limite obtenu. Enfin, nous nous sommes intéressés à la modélisation de la membrane d'un globule rouge par un fluide non-newtonien viscoélastique de Giesekus, afin d'appréhender la rhéologie du sang. Pour un problème d'interphase composé de deux fluides newtoniens (l'extérieur et l'intérieur du globule) et d'un liquide de Giesekus (la membrane du globule), nous avons dérivé formellement le problème limite, dans lequel les équations dans la membrane sont remplacées par des conditions de transmission sur une interface. / Numerical modelling and simulation of interfaces in fluid and solid mechanics are at the heart of many applications, such as cell biology (deformation of red blood cells), petroleum engineering and seismic (reservoir modelling, presence of faults, wave propagation), aerospace and civil engineering etc. This thesis focuses on the approximation of interface and interphase problems in fluid mechanics by means of the NXFEM method, which takes into account discontinuities on non-aligned meshes.We have first focused on the development of NXFEM for nonconforming finite elements in order to take into account the interface between two media. Two approaches have been proposed, for Darcy and Stokes equations. The first approach consists in modifying the basis functions of Crouzeix-Raviart on the cut cells and the second approach consists in adding some stabilization terms on each part of a cut edge. We have studied them from a theoretical and a numerical point of view. Then we have studied the asymptotic modelling and numerical approximation of interphase problems, involving a thin layer between two media. We have first considered the Darcy equations in the presence of a highly permeable fracture. By passing to the limit in the weak formulation, we have obtained an asymptotic model where the 2D fracture is described by an interface with adequate transmission conditions. A numerical method based on NXFEM with conforming finite elements has been developed for this limit problem, and its consistency and uniform stability have been proved. Numerical tests including a comparison with the literature have been presented. The asymptotic modelling has been finally extended to Stokes equations, for which we have justified the limit problem. Finally, we have considered the mechanical behaviour of red blood cells in order to better understand blood rheology. The last part of the thesis is devoted to the modelling of the membrane of a red blood cell by a non-Newtonian viscoelastic liquid, described by the Giesekus model. For an interphase problem composed of two Newtonian fluids (the exterior and the interior of the red blood cell) and a Giesekus liquid (the membrane), we formally derived the limit problem where the equations in the membrane are replaced by transmission conditions on an interface.

Ce projet de maîtrise se consacre à l’apprentissage des prépositions espagnoles chez les élèves francophones. L’identification et l’analyse des erreurs les plus fréquentes dans l’usage des prépositions par des francophones nous permettrons d’élaborer des exercices pratiques qui rendraient leur apprentissage moins difficile. Nous croyons que la difficulté dans l’utilisation des prépositions chez les étudiants réside en partie dans le fait de ne pas connaître leur emploi exact. Nous commencerons donc par présenter l’emploi des principales prépositions en espagnol à partir du Manual de la Nueva gramática de la lengua española et d’autres études. L’enseignement de la grammaire dans les cours d’espagnol comme langue étrangère (ELE) au Québec suit les règles établies par le Cadre européen commun et le Plan curricular de l’Institut Cervantès. Les étudiants développent leur compétence grammaticale de manière inductive; ils sont amenés à comprendre les règles par eux-mêmes et à créer leurs propres hypothèses qu’ils confirment ou réfutent après grâce à quelques explications formelles de l’enseignant et des exercices de pratique. Par contre, cette tendance à laisser l’apprentissage de la grammaire entre les mains des étudiants peut aussi amener à la fossilisation de leurs erreurs si les explications et la pratique ne sont pas suffisantes. Les erreurs sont perçues comme un point de départ pour comprendre où résident les difficultés des étudiants et permettent aux enseignants d’apporter les changements nécessaires à leurs méthodes d’enseignement. Notre révision de quelques investigations réalisées avec la méthode de l’analyse des erreurs, nous permet de cerner les raisons pour lesquelles les francophones commettent autant d’erreurs dans l’utilisation des prépositions espagnoles. Notre analyse de l’enseignement et de la pratique des prépositions dans trois manuels qui s’utilisent actuellement dans les cégeps et les universités du Québec nous permet de voir que les prépositions ne se pratiquent pas assez, surtout au niveau intermédiaire. Nous proposons donc des exercices pratiques qui permettront aux étudiants de pratiquer les prépositions de manière plus efficace. / This MA thesis is dedicated to the learning of the Spanish prepositions by French-speakers. We are interested in identifying and analyzing the most frequent errors in the use of the prepositions by French-speakers, which will bring us to create activities that will help them make fewer mistakes. We believe that the difficulty partly lies in the fact that students don’t know how to use them correctly. Therefore, we find it important to present the uses of the main prepositions in Spanish given by the Manual of Nueva gramática de la lengua española and other studies. The teaching of grammar in classes of Spanish as a foreign language (SFL) in Quebec follows the guidelines established by the Common European Framework and the Plan curricular of the Cervantes Institute. The students develop their grammatical competence in an inductive way; they try to understand the rules by themselves and create their own hypotheses which they will later confirm or refute thanks to some formal explanations from the teacher and practice. On the other hand, this tendency to leave the learning of the grammar mostly in the hands of the students can also bring about the fossilization of certain errors if there aren’t enough explanations or practice. The method of Error Analysis is the most effective to analyze the process of Spanish learning as a foreign language. The errors are a starting point to understand where the difficulties of the students lie and allow the teachers to bring the necessary changes in their teaching methods. Our revision of some investigations made with this method of analysis will allow us to better understand the causes of the most frequent errors French-Speakers make using Spanish prepositions. Our analysis of three textbooks used today in the classrooms of cégeps and universities of Quebec will prove that the prepositions are not practiced enough, especially in the intermediate level. We will consequently propose activities that will allow the students to practice the Spanish prepositions in a more effective way. / Este trabajo de Maestría se centra en el aprendizaje de las preposiciones españolas en alumnos francófonos. La identificación y el análisis de los errores más frecuentes nos llevarán a elaborar actividades que permitan un aprendizaje menos difícil de las preposiciones. Primero, creemos que la dificultad reside en parte en el hecho de no conocer los usos exactos de las preposiciones. Nos parece entonces importante empezar por la presentación de los usos de las principales preposiciones en español a partir del Manual de la Nueva gramática española y de otros estudios. La enseñanza de la gramática en clases de español como lengua extranjera (ELE) en Quebec sigue las mismas pautas establecidas por el Marco común europeo y el Plan curricular del Instituto Cervantes. Los estudiantes desarrollan su competencia gramatical de manera inductiva, creando hipótesis que luego confirman o refutan a partir de explicaciones formales del profesor y de práctica. Sin embargo, el hecho de dejar el aprendizaje de la gramática en las manos de los estudiantes puede causar una fosilización de los errores si no hay suficientes explicaciones y práctica. El método de análisis de los errores se reveló el más eficaz para analizar el proceso de aprendizaje de ELE. Los errores son un punto de partida para comprender dónde residen las dificultades de los estudiantes y permiten a los profesores aportar los cambios necesarios en sus métodos de enseñanza. Nuestro estudio de los errores preposicionales en la interlengua de los hablantes francófonos a partir de estudios realizados con el método de análisis de errores nos permitirá comprender mejor las causas de esos errores. Nuestro análisis de tres manuales que se utilizan actualmente en clases de ELE en los cégeps y universidades quebequenses nos permitirá ver que las preposiciones no se practican bastante en los manuales, sobre todo en el nivel intermedio, lo que podría explicar la fosilización de algunos errores. Propondremos entonces algunas actividades para que los estudiantes puedan practicar las preposiciones de una manera más eficaz.

Apesar de o Brasil ser o país com a maior comunidade japonesa fora do Japão, ainda há poucos estudos sobre a aquisição e aprendizagem do português por falantes japoneses. Partindo da descrição do sistema silábico da língua portuguesa (CÂMARA JR., 1970; FERREIRA NETTO, 2001; CRISTÓFARO SILVA, 2009; CAGLIARI, 2007; CAVALIERE, 2005) e da língua japonesa (SHIBATANI, 1987; ITÔ, 1986; McCAWLEY, 1968; HINDS, 1986), pretende-se observar por meio da Análise de Erros (CORDER, 1967) quais as estratégias utilizadas por falantes japoneses em processo de aprendizagem da língua portuguesa para pronunciar duas estruturas silábicas que não existem em sua língua materna: sílabas CVC terminadas em /r/ ou /s/, e sílabas com mais de uma consoante pré-vocálica do tipo CCV, com /r/ ou /l/ ocupando a segunda posição de ataque. A partir dessa observação, busca-se determinar quais dessas estruturas representam maior dificuldade para o aprendiz japonês. Para a composição do corpus, foram criados dezenove nomes fictícios com as estruturas silábicas em questão e sete informantes foram gravados. Ainda que não tenha sido uma pesquisa quantitativa, por meio da comparação dos resultados foi possível verificar a maior facilidade de produzir sílabas CVC em relação às CCV e, para a maioria, o número de acertos foi maior com a consoante /s/ em posição de coda e /r/ na segunda posição de ataque complexo. Quanto à estratégia utilizada, o uso de inserção vocálica foi maior que o de apagamento, exceto quando /r/ ocupa a posição de coda. A pesquisa mostrou que a dificuldade maior ou menor do aprendiz pode ser entendida a partir de processos fonológicos que acontecem na L1, no caso a língua japonesa. / Although Brazil is the country with the largest Japanese community outside Japan, there are few studies about Portuguese acquisition and learning by Japanese speakers. Based on the description of the syllabic system of the Portuguese language (CÂMARA JR., 1970; FERREIRA NETTO, 2001; CRISTÓFARO SILVA, 2009; CAGLIARI, 2007; CAVALIERE, 2005) and of the Japanese language (SHIBATANI, 1987; ITÔ, 1986; McCAWLEY, 1968; HINDS, 1986), we intend to observe through Error Analysis (CORDER, 1967) the strategies used by Japanese learners of Portuguese to pronounce two syllable structures that do not exist in their native language: CVC syllables closed by /r/ or /s/ and CCV syllables with /r/ or /l/ in the second onset position. From this observation, we seek to determine which of these structures represents more difficulty for Japanese learners. To compose the corpus, nineteen fictitious names with the syllabic structure in question were created and seven informants were recorded. Although it has not been a quantitative research, by comparing the results we could verify that it was easier to produce CVC syllables than CCV ones. In addition, for most of the informants, the number of correct production was higher with the consonant /s/ in coda position and /r/ in the second onset position. For the strategy used, the use of vowel insertion was higher than deletion, except when /r/ occupies the coda position. Research has shown that the greater or lesser difficulty of the learner can be understood from phonological processes that occur in L1, in this case the Japanese language.

Made available in DSpace on 2016-04-28T18:22:32Z (GMT). No. of bitstreams: 1 Wendel Mendes Dantas.pdf: 2248359 bytes, checksum: d5c27ce03f0a60ff11f719e7ba0ce737 (MD5) Previous issue date: 2012-05-17 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The aim of this study was to identify and classify errors found in Brazilian English learners s written tasks. The questions which guide this research are: Which are the most common errors in COBRA-7_recorte? ; What is the error variation among course levels for learners found in COBRA-7_recorte? and Which course level shows the highest error diversity in COBRA-7_recorte?". The main theoretical underpinning for the research is provided by Corpus Linguistics, an area devoted to the collection and criterious analysis of data collected from texts in electronic formar, and, specifically, by research on learner corpora. the corpora used in this research were the Corpus of Contemporary American English (COCA) (consultation corpus) and a sample of COBRA-7 (COBRA-7_recorte), the study corpus, compiled from the writings of adult learners enrolled in a network of schools which teach English as a foreign language in the state of São Paulo, and which have been produced between 2009 and 2010. The data have been collected from the institution's online server in 2011. Results have shown that the most common errors found in the analysis corpus are: wrong lexical choice, tense and aspect use, use of determiners, and wrong use of questions, negatives or auxiliaries. They have also revealed that pre-intermediate course level has the highest quantity and diversity of errors, probably because it is a level at which learners are exposed to diverse verbal tenses. Finally, this study has also shown that although wrong lexical choice, particularly the replacement of prepositions or particiles by words from the same or other grammatical categories, seem to be a problem for learners, this difficulty tends to decrease along the course, unlike errors of verbal tense and aspect use, which tend to increase / O trabalho tem como objetivo identificar e classificar os erros na escrita de aprendizes brasileiros de inglês. As perguntas que norteiam a pesquisa são: Quais os erros mais comuns no córpus COBRA-7_recorte? ; Qual a variação de erro entre os níveis de curso dos aprendizes no córpus COBRA-7_recorte? e Qual nível de curso apresenta maior diversidade de erros no córpus COBRA-7_recorte? . Esta pesquisa encontrou suporte teórico na Linguística de Córpus, área que se dedica à coleta e análise criteriosa de dados de textos em formato digital, e especificamente nas pesquisas dedicadas a córpus de aprendizes. Os córpora empregados na pesquisa foram o Corpus of Contemporary American English (COCA) (córpus de consulta) e uma amostra do COBRA-7 (córpus de estudo), compilado a partir de redações de aprendizes adultos matriculados em uma rede de escolas de inglês como língua estrangeira do estado de São Paulo, produzidas entre 2009 e 2010. Os dados foram coletados de um servidor online da própria instituição em 2011. Os resultados indicaram que os erros mais comuns encontrados no córpus de análise referem-se a: má escolha lexical, uso de tempo e aspecto verbal, uso de determinantes, e uso inadequado de questões, negações ou auxiliares. Revelaram também que o nível de curso pré-intermediário apresenta as maiores quantidade e diversidade de erros, provavelmente por se tratar de um nível no qual os aprendizes são expostos a tempos verbais diversos. Por fim, mostraram que embora a má escolha lexical, sobretudo a substituição de preposições ou conjunções por outras ou pelas mesmas classes gramaticais constitua um problema para os aprendizes, essa dificuldade diminui ao longo do curso, ao contrário do erro no uso dos tempos e aspecto verbais, que tende a aumentar