A numerical solution for the inhomogeneous Dirichlet boundary value problem on a non-convex polygon

DOI10.1016/j.amc.2018.08.011zbMath1429.65275OpenAlexW2890414948MaRDI QIDQ2007777

Hyung Jun Choi

Publication date: 22 November 2019

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2018.08.011

zbMATH Keywords

corner singularitynon-convex polygoninhomogeneous Dirichlet boundary condition

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) 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)

Cites Work

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• The Fourier finite element method for the corner singularity expansion of the heat equation
• The Fourier singular complement method for the Poisson problem. II: Axisymmetric domains
• Direct and inverse error estimates for finite elements with mesh refinements
• Elliptic boundary value problems on corner domains. Smoothness and asymptotics of solutions
• Elliptic problems in domains with piecewise smooth boundaries
• The singular complement method for 2d scalar problems
• Theory and practice of finite elements.
• On the use of singular functions with finite element approximations
• A finite element method using singular functions for Poisson equations: Mixed boundary conditions
• Finite element method for domains with corners
• The Fourier singular complement method for the Poisson problem. I: Prismatic domains
• A Finite Element Method Using Singular Functions for the Poisson Equation: Corner Singularities
• Solution Methods for the Poisson Equation with Corner Singularities: Numerical Results
• Maximum Norm Estimates in the Finite Element Method on Plane Polygonal Domains. Part 2, Refinements
• Error estimates on the coeficients obtained by the singular function method
• Finite Element Methods for Navier-Stokes Equations
• On the finite element approximation of functions with noninteger derivatives
• Coefficients of the Singularities for Elliptic Boundary Value Problems on Domains with Conical Points. III: Finite Element Methods on Polygonal Domains
• An Observation Concerning Ritz-Galerkin Methods with Indefinite Bilinear Forms
• Multigrid methods for the computation of singular solutions and stress intensity factors I: Corner singularities
• Numerical study of a new global minimizer for the Mumford-Shah functional in R³
• The Mathematical Theory of Finite Element Methods