Numerical methods for nonlinear elliptic differential equations : a synopsis /

The author proves in a systematic and unifying way stability, convergence and computing results for the different numerical methods for nonlinear elliptic problems. The proofs use linearization, compact perturbation of the coercive principal parts, or monotone operator techniques, and approximation...

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Bibliographic Details
Main Author:	Böhmer, K. (Klaus), 1936- (Author)
Format:	eBook
Language:	English
Published:	Oxford ; New York : Oxford University Press, 2010.
Series:	Numerical mathematics and scientific computation.
Subjects:	Differential equations, Elliptic > Numerical solutions. Differential equations, Nonlinear > Numerical solutions. Équations différentielles elliptiques > Solutions numériques. Équations différentielles non linéaires > Solutions numériques. MATHEMATICS > Differential Equations > Partial. Differential equations, Elliptic > Numerical solutions Differential equations, Nonlinear > Numerical solutions Electronic books.
Online Access:	Connect to the full text of this electronic book

Table of Contents:

""Contents""; ""Preface""; ""PART I: ANALYTICAL RESULTS""; ""1 From linear to nonlinear equations, fundamental results""; ""1.1 Introduction""; ""1.2 Linear versus nonlinear models""; ""1.3 Examples for nonlinear partial differential equations""; ""1.4 Fundamental results""; ""2 Elements of analysis for linear and nonlinear partial elliptic differential equations and systems""; ""2.1 Introduction""; ""2.2 Linear elliptic differential operators of second order, bilinear forms and solution concepts""; ""2.3 Bilinear forms and induced linear operators""
""2.4 Linear elliptic differential operators, Fredholm alternative and regular solutions""""2.5 Nonlinear elliptic equations""; ""2.6 Linear and nonlinear elliptic systems""; ""2.7 Linearization of nonlinear operators""; ""2.8 The Navierâ€?Stokes equation""; ""PART II: NUMERICAL METHODS""; ""3 A general discretization theory""; ""3.1 Introduction""; ""3.2 Petrovâ€?Galerkin and general discretization methods""; ""3.3 Variational and classical consistency""; ""3.4 Stability and consistency yield convergence""; ""3.5 Techniques for proving stability""; ""3.6 Stability implies invertibility""
""3.7 Solving nonlinear systems: Continuation and Newtonâ€?s method based upon the mesh independence principle (MIP)""""4 Conforming finite element methods (FEMs)""; ""4.1 Introduction""; ""4.2 Approximation theory for finite elements""; ""4.3 FEMs for linear problems""; ""4.4 Finite element methods for divergent quasilinear elliptic equations and systems""; ""4.5 General convergence theory for monotone and quasilinear operators""; ""4.6 Mixed FEMs for Navierâ€?Stokes and saddle point equations""; ""4.7 Variational methods for eigenvalue problems""; ""5 Nonconforming finite element methods""
""5.1 Introduction""""5.2 Finite element methods for fully nonlinear elliptic problems""; ""5.3 FE and other methods for nonlinear boundary conditions""; ""5.4 Quadrature approximate FEMs""; ""5.5 Consistency, stability and convergence for FEMs with variational crimes""; ""6 Adaptive finite element methods""; ""6.1 Introduction""; ""6.2 The residual error estimator for the Poisson problem""; ""6.3 Estimation of quantities of interest""; ""7 Discontinuous Galerkin methods (DCGMs)""; ""7.1 Introduction""; ""7.2 The model problem""; ""7.3 Discretization of the problem""