Stefan Kurz, Dirk Pauly, Dirk Praetorius, Sergey Repin, Daniel Sebastian
Published 2019-12-12Version 1
Functional error estimates are well-estabilished tools for a posteriori error estimation and related adaptive mesh-refinement for the finite element method (FEM). The present work proposes a first functional error estimate for the boundary element method (BEM). One key feature is that the derived error estimates are independent of the BEM discretization and provide guaranteed lower and upper bounds for the unknown error. In particular, our analysis covers Galerkin BEM as well as collocation, which makes our approach of particular interest for people working in engineering. Numerical experiments for the Laplace problem confirm the theoretical results.
Mortar coupling of $hp$-discontinuous Galerkin and boundary element methods for the Helmholtz equation
A posteriori error estimation in a finite element method for reconstruction of dielectric permittivity
A non-symmetric coupling of the finite volume method and the boundary element method
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