Numerical Approximation of Partial Differential Equations

Sören Bartels (Autor)

Buch | Softcover

XV, 535 Seiten

2018 | 1. Softcover reprint of the original 1st ed. 2016
Springer International Publishing (Verlag)
978-3-319-81265-6 (ISBN)

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Finite element methods for approximating partial differential equations have reached a high degree of maturity, and are an indispensible tool in science and technology. This textbook aims at providing a thorough introduction to the construction, analysis, and implementation of finite element methods for model problems arising in continuum mechanics. The first part of the book discusses elementary properties of linear partial differential equations along with their basic numerical approximation, the functional-analytical framework for rigorously establishing existence of solutions, and the construction and analysis of basic finite element methods. The second part is devoted to the optimal adaptive approximation of singularities and the fast iterative solution of linear systems of equations arising from finite element discretizations. In the third part, the mathematical framework for analyzing and discretizing saddle-point problems is formulated, corresponding finte element methods are analyzed, and particular applications including incompressible elasticity, thin elastic objects, electromagnetism, and fluid mechanics are addressed. The book includes theoretical problems and practical projects for all chapters, and an introduction to the implementation of finite element methods.

Sören Bartels is Professor of Applied Mathematics at the Albert-Ludwigs University in Freiburg, Germany. His primary research interest is in the development and analysis of approximation schemes for nonlinear partial differential equations with applications in the simulation of modern materials. Professor Bartels has published the Springer textbook "Numerik 3x9" and the monograph "Numerical methods for nonlinear partial differential equations" in the Springer Series in Computational Mathematics.

Preface.- Part I Finite differences and finite elements.- Elliptic partial differential equations.- Finite Element Method.- Part II Local resolution and iterative solution.- Local Resolution Techniques.- Iterative Solution Methods.- Part III Constrained and singularly perturbed problems.- Saddled-point Problems.- Mixed and Nonstandard methods.- Applications.- Problems and Projects.- Implementation aspects.- Notations, inequalities, guidelines.- Index

Erscheinungsdatum	05.03.2022
Reihe/Serie	Texts in Applied Mathematics
Zusatzinfo	XV, 535 p. 170 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	8248 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	convergence analysis • Finite Element Methods • iterative solution methods • Numerical analysis • Partial differential equations
ISBN-10	3-319-81265-3 / 3319812653
ISBN-13	978-3-319-81265-6 / 9783319812656
Zustand	Neuware