\(L^2\)-error estimates for Dirichlet and Neumann problems on anisotropic finite element meshes

DOI10.1007/s10492-011-0002-7zbMath1224.65252OpenAlexW2079549226MaRDI QIDQ548580

Dieter Sirch, Thomas Apel

Publication date: 29 June 2011

Published in: Applications of Mathematics (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/116520

zbMATH Keywords

elliptic boundary value problema priori error estimatenon-convex domainedge singularityanisotropic mesh gradingDirichlet and a Neumann boundary value problemfinite element errorinterpolation of non-smooth functions

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical interpolation (65D05) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)

Related Items (11)

Elliptic boundary value problems with Gaussian white noise loads ⋮ High accuracy analysis of an \(H^1\)-Galerkin mixed finite element method for two-dimensional time fractional diffusion equations ⋮ A Priori Mesh Grading for Distributed Optimal Control Problems ⋮ Anisotropic linear triangle finite element approximation for multi-term time-fractional mixed diffusion and diffusion-wave equations with variable coefficient on 2D bounded domain ⋮ High-accuracy finite element method for 2D time fractional diffusion-wave equation on anisotropic meshes ⋮ Finite element error estimates for Neumann boundary control problems on graded meshes ⋮ Optimal control of the Stokes equations: conforming and non-conforming finite element methods under reduced regularity ⋮ Local mesh refinement for the discretization of Neumann boundary control problems on polyhedra ⋮ High Accuracy Analysis of an Anisotropic Nonconforming Finite Element Method for Two-Dimensional Time Fractional Wave Equation ⋮ Finite element error estimates on the boundary with application to optimal control ⋮ Nonconforming quasi-Wilson finite element method for 2D multi-term time fractional diffusion-wave equation on regular and anisotropic meshes

Cites Work

• Approximation of a class of optimal control problems with order of convergence estimates
• Neumann problem for second-order elliptic equations in domains with edges on the boundary
• Error estimates for the numerical approximation of boundary semilinear elliptic control prob\-lems
• Convergence of approximations vs. regularity of solutions for convex, control-constrained optimal-control problems
• Anisotropic interpolation with applications to the finite element method
• Neumann and mixed problems on curvilinear polyhedra
• Elliptic problems in domains with piecewise smooth boundaries
• Finite element method for elliptic problems with edge singularities
• A variational discretization concept in control constrained optimization: The linear-quadratic case
• Error estimates for the numerical approximation of a semilinear elliptic control problem
• Singular behavior of elliptic problems in non Hilbertian Sobolev spaces
• The asymptotics of the solutions of linear elliptic variational problems in domains with edges
• Finite element treatment of boundary singularities by augmentation with non-exact singular functions
• Finite Element Interpolation of Nonsmooth Functions Satisfying Boundary Conditions
• On the approximation of the solution of an optimal control problem governed by an elliptic equation
• Mesh Refinement and Windowing Near Edges for Some Elliptic Problem
• Superconvergence Properties of Optimal Control Problems
• Interpolation of non-smooth functions on anisotropic finite element meshes
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: \(L^2\)-error estimates for Dirichlet and Neumann problems on anisotropic finite element meshes