On the finite element method for elliptic problems with degenerate and singular coefficients

DOI10.1090/S0025-5718-06-01910-7zbMath1112.65116OpenAlexW1554959944MaRDI QIDQ3426012

Daniel Arroyo, Norbert Heuer, Alexei Bespalov

Publication date: 7 March 2007

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

Full work available at URL: https://doi.org/10.1090/s0025-5718-06-01910-7

zbMATH Keywords

numerical resultsfinite element methodsecond-order elliptic equationsCoulomb fieldproblems with singularities

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) Degenerate elliptic equations (35J70)

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A cell-centered finite difference method for a degenerate elliptic equation arising from two-phase mixtures ⋮ Piecewise polynomial interpolation in Muckenhoupt weighted Sobolev spaces and applications ⋮ The optimal convergence of finite element methods for the three-dimensional second-order elliptic boundary value problem with singularity ⋮ On differential properties of the \(R_\nu\)-generalized solution of the Dirichlet problem with coordinated degeneration of the input data ⋮ On the existence and uniqueness of \(R_v\)-generalized solution for Dirichlet problem with singularity on all boundary ⋮ On the Error Estimation of the Finite Element Method for the Boundary Value Problems with Singularity in the Lebesgue Weighted Space ⋮ A weighted least squares finite element method for elliptic problems with degenerate and singular coefficients ⋮ Multilevel methods for nonuniformly elliptic operators and fractional diffusion ⋮ The finite element method for a boundary value problem with strong singularity ⋮ Unnamed Item ⋮ A Linear Degenerate Elliptic Equation Arising from Two-Phase Mixtures ⋮ Analysis of Schrödinger operators with inverse square potentials II: FEM and approximation of eigenfunctions in the periodic case

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• Galerkin Methods for Singular Boundary Value Problems in One Space Dimension
• Improved Accuracy by Adapted Mesh-Refinements in the Finite Element Method
• Ritz–Galerkin Methods for Singular Boundary Value Problems

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