Multilevel finite element approximation

Inhaltsverzeichnis1 Introduction.2 Finite element approximation.2.1 Finite elements, multivariate splines, wavelets.2.2 Moduli of smoothness and K-functionals.2.3 Jackson and Whitney inequalities.2.4 Bernstein inequalities and inverse estimates.2.5 Information on other approximation schemes.2.6 Constructive characterization of Besov spaces.3 Function spaces.3.1 Spaces on Rd.3.2 Spaces on domains and extension.3.3 Spaces on manifolds and traces.3.4 Approximation spaces on polyhedral domains.4 Applications to multilevel methods.4.1 The abstract Schwarz theory.4.2 Second-order elliptic equations.4.3 The biharmonic problem.4.4 Domain decomposition and boundary element methods.4.5 Sparse grids.4.6 Nonconforming and mixed methods.5 Error estimates and adaptivity.5.1 Traditional error estimates.5.2 h-version and nonlinear approximation.5.3 Adaptive multilevel methods.5.4 More complicated approximation schemes.References.