Numerical Approximation of Partial Differential Equations

Sören Bartels

ISBN 10: 3319812653 / ISBN 13: 9783319812656

Editore: Springer International Publishing AG, CH, 2018

Riguardo questo articolo

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. Softcover reprint of the original 1st ed. 2016.

Codice articolo LU-9783319812656

Dati bibliografici

• Titolo: Numerical Approximation of Partial Differential Equations
• Editore: Springer International Publishing AG, CH
• Data di pubblicazione: 2018
• Lingua: Inglese
• ISBN 10: 3319812653
• ISBN 13: 9783319812656
• Rilegatura: Paperback
• Condizione: New

Descrizione articolo

Riassunto

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.

Informazioni sull?autore

Sören Bartels is Professor of Applied Mathematicsat the Albert-Ludwigs University in Freiburg, Germany. His primaryresearch interest is in the development and analysis of approximation schemesfor nonlinear partial differential equations with applications in thesimulation of modern materials. Professor Bartels has published the Springertextbook "Numerik 3x9" and the monograph "Numerical methods for nonlinearpartial differential equations" in the Springer Series in ComputationalMathematics.