Discretization of the Poisson equation with non-smooth data and emphasis on non-convex domains

DOI10.1002/num.22057zbMath1353.65117arXiv1505.01229OpenAlexW2962921361WikidataQ115398086 ScholiaQ115398086MaRDI QIDQ2821188

Thomas Apel, Serge Nicaise, Johannes Pfefferer

Publication date: 16 September 2016

Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1505.01229

zbMATH Keywords

convergencenumerical examplefinite element methodregularizationerror estimatePoisson equationpolygonal domainnon-smooth datavery weak formulationmethod of transposition

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

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Local convergence of the boundary element method on polyhedral domains ⋮ Optimal Dirichlet control of partial differential equations on networks ⋮ On the Regularity of the Solutions of Dirichlet Optimal Control Problems in Polygonal Domains ⋮ Stability of the Laplace Single Layer Boundary Integral Operator in Sobolev Spaces ⋮ An error estimate for finite element approximation to elliptic PDEs with discontinuous Dirichlet boundary data ⋮ Finite element approximations for PDEs with irregular Dirichlet boundary data on boundary concentrated meshes ⋮ Error estimates for Dirichlet control problems in polygonal domains: quasi-uniform meshes ⋮ A finite element method for elliptic Dirichlet boundary control problems ⋮ Analysis of Finite Element Approximations of Stokes Equations with NonSmooth Data ⋮ The halfspace matching method: a new method to solve scattering problems in infinite media ⋮ Two fast finite difference schemes for elliptic Dirichlet boundary control problems ⋮ Sparse Dirichlet optimal control problems ⋮ Adapted Numerical Methods for the Poisson Equation with $L^2$ Boundary Data in NonConvex Domains ⋮ External optimal control of nonlocal PDEs ⋮ Finite Element Error Estimates for Normal Derivatives on Boundary Concentrated Meshes ⋮ An ultraweak space-time variational formulation for the wave equation: Analysis and efficient numerical solution

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