We present three new stabilized finite element (FE) based Petrov-Galerkin methods for the convection-diffusionreaction (CDR), the Helmholtz and the Stokes problems, respectively. The work embarks upon a priori analysis of a consistency recovery procedure for some stabilization methods belonging to the Petrov- Galerkin framework. It was ound that the use of some standard practices (e.g. M-Matrices theory) for the design of essentially non-oscillatory numerical methods is not appropriate when consistency recovery methods are employed. Hence, with respect to convective stabilization, such recovery methods are not preferred. Next, we present the design of a high-resolution Petrov-Galerkin (HRPG) method for the CDR problem. The structure of the method in 1 D is identical to the consistent approximate upwind (CAU) Petrov-Galerkin method [doi: 10.1016/0045-7825(88)90108-9] except for the definitions of he stabilization parameters. Such a structure may also be attained via the Finite Calculus (FIC) procedure [doi: 10.1 016/S0045-7825(97)00119-9] by an appropriate definition of the characteristic length. The prefix high-resolution is used here in the sense popularized by Harten, i.e. second order accuracy for smooth/regular regimes and good shock-capturing in non-regular re9jmes. The design procedure in 1 D embarks on the problem of circumventing the Gibbs phenomenon observed in L projections. Next, we study the conditions on the stabilization parameters to ircumvent the global oscillations due to the convective term. A conjuncture of the two results is made to deal with the problem at hand that is usually plagued by Gibbs, global and dispersive oscillations in the numerical solution. A multi dimensional extension of the HRPG method using multi-linear block finite elements is also presented. Next, we propose a higher-order compact scheme (involving two parameters) on structured meshes for the Helmholtz equation. Making the parameters equal, we recover the alpha-interpolation of the Galerkin finite element method (FEM) and the classical central finite difference method. In 1 D this scheme is identical to the alpha-interpolation method [doi: 10.1 016/0771 -050X(82)90002-X] and in 2D choosing the value 0.5 for both the parameters, we recover he generalized fourth-order compact Pade approximation [doi: 10.1 006/jcph.1995.1134, doi: 10.1016/S0045- 7825(98)00023-1] (therein using the parameter V = 2). We follow [doi: 10.1 016/0045-7825(95)00890-X] for the analysis of this scheme and its performance on square meshes is compared with that of the quasi-stabilized FEM [doi: 10.1016/0045-7825(95)00890-X]. Generic expressions for the parameters are given that guarantees a dispersion accuracy of sixth-order should the parameters be distinct and fourth-order should they be equal. In the later case, an expression for the parameter is given that minimizes the maximum relative phase error in 2D. A Petrov-Galerkin ormulation that yields the aforesaid scheme on structured meshes is also presented. Convergence studies of the error in the L2 norm, the H1 semi-norm and the I ~ Euclidean norm is done and the pollution effect is found to be small. / Presentamos tres nuevos metodos estabilizados de tipo Petrov- Galerkin basado en elementos finitos (FE) para los problemas de convecci6n-difusi6n- reacci6n (CDR), de Helmholtz y de Stokes, respectivamente. El trabajo comienza con un analisis a priori de un metodo de recuperaci6n de la consistencia de algunos metodos de estabilizaci6n que pertenecen al marco de Petrov-Galerkin. Hallamos que el uso de algunas de las practicas estandar (por ejemplo, la eoria de Matriz-M) para el diserio de metodos numericos esencialmente no oscilatorios no es apropiado cuando utilizamos los metodos de recu eraci6n de la consistencia. Por 10 tanto, con res ecto a la estabilizaci6n de conveccion, no preferimos tales metodos de recuperacion . A continuacion, presentamos el diser'io de un metodo de Petrov-Galerkin de alta-resolucion (HRPG) para el problema CDR. La estructura del metodo en 10 es identico al metodo CAU [doi: 10.1016/0045-7825(88)90108-9] excepto en la definicion de los parametros de estabilizacion. Esta estructura tambien se puede obtener a traves de la formulacion del calculo finito (FIC) [doi: 10.1 016/S0045- 7825(97)00119-9] usando una definicion adecuada de la longitud caracteristica. El prefijo de "alta-resolucion" se utiliza aqui en el sentido popularizado por Harten, es decir, tener una solucion con una precision de segundo orden en los regimenes suaves y ser esencialmente no oscilatoria en los regimenes no regulares. El diser'io en 10 se embarca en el problema de eludir el fenomeno de Gibbs observado en las proyecciones de tipo L2. A continuacion, estudiamos las condiciones de los parametros de estabilizacion para evitar las oscilaciones globales debido al ermino convectivo. Combinamos los dos resultados (una conjetura) para tratar el problema COR, cuya solucion numerica sufre de oscilaciones numericas del tipo global, Gibbs y dispersiva. Tambien presentamos una extension multidimensional del metodo HRPG utilizando los elementos finitos multi-lineales. fa. continuacion, proponemos un esquema compacto de orden superior (que incluye dos parametros) en mallas estructuradas para la ecuacion de Helmholtz. Haciendo igual ambos parametros, se recupera la interpolacion lineal del metodo de elementos finitos (FEM) de tipo Galerkin y el clasico metodo de diferencias finitas centradas. En 10 este esquema es identico al metodo AIM [doi: 10.1 016/0771 -050X(82)90002-X] y en 20 eligiendo el valor de 0,5 para ambos parametros, se recupera el esquema compacto de cuarto orden de Pade generalizada en [doi: 10.1 006/jcph.1 995.1134, doi: 10.1 016/S0045-7825(98)00023-1] (con el parametro V = 2). Seguimos [doi: 10.1 016/0045-7825(95)00890-X] para el analisis de este esquema y comparamos su rendimiento en las mallas uniformes con el de "FEM cuasi-estabilizado" (QSFEM) [doi: 10.1016/0045-7825 (95) 00890-X]. Presentamos expresiones genericas de los para metros que garantiza una precision dispersiva de sexto orden si ambos parametros son distintos y de cuarto orden en caso de ser iguales. En este ultimo caso, presentamos la expresion del parametro que minimiza el error maxima de fase relativa en 20. Tambien proponemos una formulacion de tipo Petrov-Galerkin ~ue recupera los esquemas antes mencionados en mallas estructuradas. Presentamos estudios de convergencia del error en la norma de tipo L2, la semi-norma de tipo H1 y la norma Euclidiana tipo I~ y mostramos que la perdida de estabilidad del operador de Helmholtz ("pollution effect") es incluso pequer'ia para grandes numeros de onda. Por ultimo, presentamos una coleccion de metodos FE estabilizado para el problema de Stokes desarrollados a raves del metodo FIC de primer orden y de segundo orden. Mostramos que varios metodos FE de estabilizacion existentes y conocidos como el metodo de penalizacion, el metodo de Galerkin de minimos cuadrados (GLS) [doi: 10.1016/0045-7825(86)90025-3], el metodo PGP (estabilizado a traves de la proyeccion del gradiente de presion) [doi: 10.1 016/S0045-7825(96)01154-1] Y el metodo OSS (estabilizado a traves de las sub-escalas ortogonales) [doi: 10.1016/S0045-7825(00)00254-1] se recuperan del marco general de FIC. Oesarrollamos una nueva familia de metodos FE, en adelante denominado como PLS (estabilizado a traves del Laplaciano de presion) con las formas no lineales y consistentes de los parametros de estabilizacion. Una caracteristica distintiva de la familia de los metodos PLS es que son no lineales y basados en el residuo, es decir, los terminos de estabilizacion dependera de los residuos discretos del momento y/o las ecuaciones de incompresibilidad. Oiscutimos las ventajas y desventajas de estas tecnicas de estabilizaci6n y presentamos varios ejemplos de aplicacion

Η Ηλεκτροχημική Ενίσχυση της Κατάλυσης (ή φαινόμενο NEMCA) είναι ένα φαινόμενο όπου εφαρμογή μικρών ρευμάτων ή δυναμικών (±2 V) μπορεί να τροποποιήσει την ενεργότητα καταλυτών υποστηριγμένων σε ιοντικούς ή μικτούς ιοντικούς-ηλεκτρονικούς αγωγούς, να επηρεάσει την εκλεκτικότητα σε επιθυμητή κατεύθυνση και να μεταβάλλει τις ηλεκτρονικές και συνεπώς τις καταλυτικές ιδιότητες με τρόπο ελεγχόμενο, αντιστρεπτό και σε κάποιο βαθμό προβλέψιμο. Στην παρούσα διατριβή μελετήθηκε η επίδραση του πάχους του καταλυτικού υμενίου στο μέγεθος της ηλεκτροχημικής ενίσχυσης, χρησιμοποιώντας την αντίδραση της οξείδωσης του C2H4 σε πορώδη υμένια Pt πάχους μεταξύ 0.2 και 1.4 μm, εναποτεθειμένα με τη μέθοδο επάλειψης οργανομεταλλικής πάστας, σε στερεό ηλεκτρολύτη YSZ, έναν αγωγό ιόντων Ο2-. Βρέθηκε πως η αύξηση του πάχους των υμενίων που χρησιμοποιούνται στις μελέτες ηλεκτροχημικής ενίσχυσης, προκαλεί μείωση στο λόγο προσαύξησης του ρυθμού, ρ, συμπεριφορά που βρίσκεται σε καλή συμφωνία με τις αναλυτικές προβλέψεις του μαθηματικού μοντέλου που περιγράφει την επιφανειακή διάχυση-αντίδραση των προωθητικών ειδών. Με βάση τις επιτυχείς μελέτες ηλεκτροχημικής ενίσχυσης που έχουν πραγματοποιηθεί σε λεπτά (40 nm), εναποτεθειμένα με τη μέθοδο της ιοντοβολής (sputtering) καταλυτικά υμένια, έγινε επέκταση της μελέτης της επίδρασης του πάχους σε τόσο λεπτά υμένια. Συγκεκριμένα, εξετάσθηκε η καταλυτική και η ηλεκτροχημικά ενισχυμένη συμπεριφορά πολύ λεπτών (30-90 nm) καταλυτικών υμενίων εναποτεθειμένων με τη μέθοδο του sputtering, τη μέθοδο Pulsed Laser Deposition και την τεχνική εναπόθεσης με ατμό (vapor deposition). Τιμές του λόγου προσαύξησης του ρυθμού, ρ, έως και 440 και τιμές φαρανταϊκής απόδοσης, Λ, έως και 1000 παρατηρήθηκαν για τα υμένια που εναποτέθηκαν με τη μέθοδο του sputtering. Η διασπορά μετάλλου στα υμένια αυτά είναι έως και 20%, συγκρίσιμη δηλαδή με αυτή των εμπορικών υποστηριγμένων καταλυτών. Τέλος, παρουσιάζεται η λειτουργία ενός πρόσφατα ανεπτυγμένου μονολιθικού ηλεκτροχημικά ενισχυόμενου αντιδραστήρα (MEPR), χρησιμοποιώντας την περιβαλλοντικού ενδιαφέροντος αντίδραση της αναγωγής του ΝΟ από αιθυλένιο παρουσία Ο2. Χρησιμοποιώντας καταλυτικά στοιχεία τύπου Pt-Rh(1:1)/YSZ/Au, παρουσία 10% Ο2 και σε ογκομετρικές παροχές έως και 1000 cc/min, ο αντιδραστήρας λειτούργησε επιδεικνύοντας τιμές φαρανταϊκής απόδοσης που ξεπερνούν τη μονάδα και επιτυγχάνοντας 50% και 44% προσαύξηση στους ρυθμούς μετατροπής του καυσίμου και του ΝΟ αντίστοιχα. Αυτή η μελέτη είναι η πρώτη που επιδεικνύει ηλεκτροχημική ενίσχυση της αντίδρασης αναγωγής του NO σε τόσο υψηλές τιμές μερικής πίεσης οξυγόνου (10% O2), που είναι αντιπροσωπευτικές για εξατμίσεις μηχανών πτωχού καυσίμου και μηχανών Diesel. Ο MEPR αποδεσμεύει το φαινόμενο NEMCA από την έως σήμερα χρήση του στην καθαρά εργαστηριακή κλίμακα και δείχνει πολλά υποσχόμενος για την πρακτική εφαρμογή του φαινομένου. / The effect of Electrochemical Promotion of Catalysis (EPOC or NEMCA effect) is a phenomenon where application of small currents or potentials (±2 V) alters the activity and selectivity of catalysts supported on ionic or mixed ionic-electronic conductors and modifies the electronic and thus catalytic properties in a controllable, reversible and to some extent predictable manner. The effect of catalyst film thickness on the magnitude of electrochemical promotion (ρ and Λ values) has not been studied experimentally so far but a mathematical model has been developed, accounting for surface diffusion and reaction of the promoting species, which predicts a strong variation of ρ and Λ with catalyst film thickness L. In the present thesis is examined for the first time experimentally the effect of catalyst film thickness on the magnitude of the EPOC, using porous Pt catalyst-electrodes prepared from Engelhard Pt paste with thicknesses in the range 0.2 to 1.4 μm. It was found that increasing the thickness of porous catalyst films used in electrochemical promotion studies causes a decrease in the rate enhancement ratio, ρ, due to the gradual axial decrease from the three-phase-boundaries to the top of the film of the surface concentration of the promoting backspillover O2- species which diffuse and react on the porous catalyst surface. Increasing film thickness causes a moderate increase in the Faradaic efficiency, Λ, which can be predicted by the parameter 2Fro/I0. The ρ and Λ behaviour is in good agreement with the analytical model prediction and provides additional support for the O2- promoter reaction-diffusion model and for the sacrificial promoter mechanism of electrochemical promotion. Most electrochemical promotion studies have been carried out so far with thick (0.1 μm to 5 μm) porous metal catalyst films with a roughness factor of the order of 500 and small (typically less than 0.1%) metal dispersion, deposited on solid electrolytes using a variety of deposition techniques. Very recently, electropromotion studies have been extended to thin (40 nm) sputter coated porous metal catalysts with metal dispersion of the order of 10 to 30%. The effect of thickness with such thin (30 to 90 nm) sputtered Pt catalyst-electrodes on the magnitude of electrochemical promotion is discussed, as well as the effect of the catalyst deposition method (Sputtering, Pulsed Laser Deposition and Vapor Deposition) using the model reaction of ethylene oxidation. Rate enhancement ratio, ρ, values up to 440 and Λ values up to 1000 where obtained for the sputtered films, in agreement with the sacrificial promoter and diffusion-reaction models of EPOC which predict increase in ρ value with thinner films. An environmental interest reaction, the reduction of NO by ethylene in the presence of excess oxygen, was investigated in a recently developed MEPR. In this novel dismantlable monolithic-type electrochemically promoted catalytic reactor, thin (~40 nm) porous catalyst films are sputter-deposited on thin (0.25 mm) parallel solid electrolyte plates supported in the grooves of a ceramic monolithic holder and serve as electropromoted catalyst elements. Using Pt-Rh(1:1)/YSZ/Au-type catalyst elements, the 8-plate reactor operated with apparent Faradaic efficiency exceeding unity achieving significant and reversible enhancement in the rates of C2H4 and NO consumption in presence of up to 10% O2 in the feed at gas flow rates up to 1000 cc/min. The Pt-Rh co-sputtered films exhibited very good performance in terms of stability and selectivity for N2 formation, i.e. practically 100% under all reaction conditions. The reactor, which is a hybrid between a monolithic catalytic reactor and a flat-plate solid oxide fuel cell, permits easy practical utilization of the electrochemical promotion of catalysis.

Problems governed by partial differential equations (PDEs) in deformable domains, t Rd; d = 2; 3; are of fundamental importance in science and engineering. They are of particular relevance in the design of many engineering systems e.g., aircrafts and bridges as well as to the analysis of several biological phenomena e.g., blood ow in arteries. However, developing numerical scheme for such problems is still very challenging even when the deformation of the boundary of domain is prescribed a priori. Possibility of excessive mesh distortion is one of the major challenge when solving such problems with numerical methods using boundary tted meshes. The arbitrary Lagrangian- Eulerian (ALE) approach is a way to overcome this difficulty. Numerical simulations of convection-dominated problems have for long been the subject to many researchers. Galerkin formulations, which yield the best approximations for differential equations with high diffusivity, tend to induce spurious oscillations in the numerical solution of convection dominated equations. Though such spurious oscillations can be avoided by adaptive meshing, which is computationally very expensive on ne grids. Alternatively, stabilization methods can be used to suppress the spurious oscillations. In this work, the considered equation is designed within the framework of ALE formulation. In the first part, Streamline Upwind Petrov-Galerkin (SUPG) finite element method with conservative ALE formulation is proposed. Further, the first order backward Euler and the second order Crank-Nicolson methods are used for the temporal discretization. It is shown that the stability of the semi-discrete (continuous in time) ALE-SUPG equation is independent of the mesh velocity, whereas the stability of the fully discrete problem is unconditionally stable for implicit Euler method and is only conditionally stable for Crank-Nicolson time discretization. Numerical results are presented to support the stability estimates and to show the influence of the SUPG stabilization parameter in a time-dependent domain. In the second part of this work, SUPG stabilization method with non-conservative ALE formulation is proposed. The implicit Euler, Crank-Nicolson and backward difference methods are used for the temporal discretization. At the discrete level in time, the ALE map influences the stability of the corresponding discrete scheme with different time discretizations, and it leads to schemes where conservative and non-conservative formulations are no longer equivalent. The stability of the fully discrete scheme, irrespective of the temporal discretization, is only conditionally stable. It is observed from numerical results that the Crank-Nicolson scheme induces high oscillations in the numerical solution compare to the implicit Euler and the backward difference time discretiza-tions. Moreover, the backward difference scheme is more sensitive to the stabilization parameter k than the other time discretizations. Further, the difference between the solutions obtained with the conservative and non-conservative ALE forms is significant when the deformation of domain is large, whereas it is negligible in domains with small deformation. Finally, the local projection stabilization (LPS) and the higher order dG time stepping scheme are studied for convection dominated problems. The analysis is based on the quadrature formula for approximating the integrals in time. We considered the exact integration in time, which is impractical to implement and the Radau quadrature in time, which can be used in practice. The stability and error estimates are shown for the mathematical basis of considered numerical scheme with both time integration methods. The numerical analysis reveals that the proposed stabilized scheme with exact integration in time is unconditionally stable, whereas Radau quadrature in time is conditionally stable with time-step restriction depending on the ALE map. The theoretical estimates are illustrated with appropriate numerical examples with distinct features. The second order dG(1) time discretization is unconditionally stable while Crank-Nicolson gives the conditional stable estimates only. The convergence order for dG(1) is two which supports the error estimate.

No description available.