Numerical Approximation of Partial Differential Equations

Anglický jazyk

Numerical Approximation of Partial Differential Equations

Vydavateľstvo: Springer International Publishing
Rok vydania: 2016
Formát: Hardback
Rozmer: 241 x 160 mm
Jazyk: Anglický jazyk
ISBN: 9783319323534

Na objednávku

84.14 €

bežná cena: 93.49 €

O knihe

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.