Multilevel Finite Element Approximation

Inhaltsverzeichnis

• 1 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.