Adaptive Boundary Element Methods

Abstract

This paper reviews the state of the art and discusses very recent mathematical developments in the field of adaptive boundary element methods. This includes an overview of available a posteriori error estimates as well as a state-of-the-art formulation of convergence and quasi-optimality of adaptive mesh-refining algorithms.

References in corpus (4)

• Axioms of Adaptivity
• Each H^{1/2}-stable projection yields convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data in R^d
• Convergence and Quasi-Optimality of Adaptive FEM with Inhomogeneous Dirichlet Data
• ZZ-type aposteriori error estimators for adaptive boundary element methods on a curve

Cited by in corpus (8)

• An adaptive IGA-BEM with hierarchical B-splines based on quasi-interpolation quadrature schemes
• Optimal convergence for adaptive IGA boundary element methods for weakly-singular integral equations
• Adaptive boundary element methods for the computation of the electrostatic capacity on complex polyhedra
• Adaptive BEM for elliptic PDE systems, part II: Isogeometric analysis with hierarchical B-splines for weakly-singular integral equations
• An adaptive boundary element method for the transmission problem with hyperbolic metamaterials
• Higher-order accurate diffuse-domain methods for partial differential equations with Dirichlet boundary conditions in complex, evolving geometries
• Adaptive time-domain boundary element methods for the wave equation with Neumann boundary conditions
• Optimal convergence rates of an adaptive hybrid FEM-BEM method for full-space linear transmission problems