Beschreibung der Finite Elemente Software-Familie SPC-PM3-AdH-XX für: (S)cientific (P)arallel (C)omputing - (P)rogramm-(M)odul (3)D (ad)aptiv (H)exaederelemente. Für XX stehen die einzelnen Spezialvarianten, die in Teil 2 detailliert geschildert werden. Stand: Ende 2013

Beschreibung der Finite Elemente Software-Familie SPC-PM3-AdH-XX für: (S)cientific (P)arallel (C)omputing - (P)rogramm-(M)odul (3)D (ad)aptiv (H)exaederelemente. Für XX stehen die einzelnen Spezialvarianten, die in Teil 2 detailliert geschildert werden. Stand: Ende 2013

In the field of singularly perturbed reaction- or convection-diffusion boundary value problems the research area of a priori error analysis for the finite element method, has already been thoroughly investigated. In particular, for mesh adapted methods and/or various stabilization techniques, works have been done that prove optimal rates of convergence or supercloseness uniformly in the perturbation parameter epsilon. Commonly, however, it is assumed that the exact solution behaves nicely in that it obeys certain regularity assumptions although in general, e.g. due to corner singularities, these regularity requirements are not satisfied. So far, insufficient regularity has been met by assuming compatibility conditions on the data. The present thesis originated from the question: What can be shown if these rather unrealistic additional assumptions are dropped? We are interested in epsilon-uniform a priori estimates for convergence and superconvergence that include some regularity parameter that is adjustable to the smoothness of the exact solution. A major difficulty that occurs when seeking the numerical error decay is that the exact solution is not known. Since we strive for reliable rates of convergence we want to avoid the standard approach of the "double-mesh principle". Our choice is to use reference solutions as a substitute for the exact solution. Numerical experiments are intended to confirm the theoretical results and to bring further insights into the interplay between layers and singularities. To computationally realize the thereby arising demanding practical aspects of the finite element method, a new software is developed that turns out to be particularly suited for the needs of the numerical analyst. Its design, features and implementation is described in detail in the second part of the thesis.

This diploma thesis deals with the proposal of 3D model of single SI engine designated for research purposes. The work is mainly concentrated on the construction of the engine composition that consists of crank case, crankshaft and balance unit. It contains the research of experimental engines and constructions of basic parts of standard SI engines. The aim is the proposal of all-purpose construction of crank case and the following control with the help of FEM system.

Beschreibung der Finite Elemente Software-Familie SPC-PM3-AdH-XX für: (S)cientific (P)arallel (C)omputing - (P)rogramm-(M)odul (3)D (ad)aptiv (H)exaederelemente. Für XX stehen die einzelnen Spezialvarianten, die in Teil 2 detailliert geschildert werden. Stand: Ende 2013:1 Allgemeine Vorbemerkungen 2 Grundstruktur 3 Datenstrukturen 4 Gesamtablauf 5 Parallelisierung 6 Die Grundvariante A3D_Original und ihre Bibliotheken

Beschreibung der Finite Elemente Software-Familie SPC-PM3-AdH-XX für: (S)cientific (P)arallel (C)omputing - (P)rogramm-(M)odul (3)D (ad)aptiv (H)exaederelemente. Für XX stehen die einzelnen Spezialvarianten, die in Teil 2 detailliert geschildert werden. Stand: Ende 2013:1 Vorbemerkungen 2 Probleme mit transversal-isotropem Material 3 Gleichungen vom Sattelpunktstyp 4 Probleme der Thermo-Elastizität 5 Nichtlineare Probleme der großen Deformationen

In the field of singularly perturbed reaction- or convection-diffusion boundary value problems the research area of a priori error analysis for the finite element method, has already been thoroughly investigated. In particular, for mesh adapted methods and/or various stabilization techniques, works have been done that prove optimal rates of convergence or supercloseness uniformly in the perturbation parameter epsilon. Commonly, however, it is assumed that the exact solution behaves nicely in that it obeys certain regularity assumptions although in general, e.g. due to corner singularities, these regularity requirements are not satisfied. So far, insufficient regularity has been met by assuming compatibility conditions on the data. The present thesis originated from the question: What can be shown if these rather unrealistic additional assumptions are dropped? We are interested in epsilon-uniform a priori estimates for convergence and superconvergence that include some regularity parameter that is adjustable to the smoothness of the exact solution. A major difficulty that occurs when seeking the numerical error decay is that the exact solution is not known. Since we strive for reliable rates of convergence we want to avoid the standard approach of the "double-mesh principle". Our choice is to use reference solutions as a substitute for the exact solution. Numerical experiments are intended to confirm the theoretical results and to bring further insights into the interplay between layers and singularities. To computationally realize the thereby arising demanding practical aspects of the finite element method, a new software is developed that turns out to be particularly suited for the needs of the numerical analyst. Its design, features and implementation is described in detail in the second part of the thesis.