6533b82bfe1ef96bd128e1b0
RESEARCH PRODUCT
Functional a posteriori error estimates for boundary element methods
Daniel SebastianSergey RepinSergey RepinDirk PraetoriusDirk PaulyStefan Kurzsubject
osittaisdifferentiaaliyhtälötDiscretizationApplied MathematicsComputationNumerical analysisNumerical Analysis (math.NA)adaptive mesh-refinementFinite element methodMathematics::Numerical Analysisboundary element methodComputational MathematicsComputer Science::Computational Engineering Finance and ScienceCollocation methodMathematikFOS: MathematicsApplied mathematicsA priori and a posterioriMathematics - Numerical Analysisnumeerinen analyysivirheanalyysiGalerkin methodBoundary element methodfunctional a posteriori error estimate65N38 65N15 65N50Mathematicsdescription
Functional error estimates are well-established 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 and the collocation method, what makes the approach of particular interest for scientific computations and engineering applications. Numerical experiments for the Laplace problem confirm the theoretical results.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2019-12-12 | Numerische Mathematik |