Comparison of two methods for the computation of singular solutions in elliptic problems

DOI10.1016/S0377-0427(96)00173-2zbMath0880.65083MaRDI QIDQ1357001

Andreas Poullikkas, Georgios C. Georgiou, Andreas G. Boudouvis

Publication date: 8 January 1998

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

zbMATH Keywords

stabilityfinite element methodsElliptic problemssingular function boundary integral methodBoundary singularitiesCracked beam problemintegrated singular basis function method

Mathematics Subject Classification ID

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)

Related Items (11)

Singularities and regularity of stationary Stokes and Navier-Stokes equations on polygonal domains and their treatments ⋮ The singular function boundary integral method for an elastic plane stress wedge beam problem with a point boundary singularity ⋮ The solution of Laplacian problems over L-shaped domains with a singular function boundary integral method ⋮ On solving the cracked‐beam problem by block method ⋮ Model order reduction for meshfree solution of Poisson singularity problems ⋮ The singular function boundary integral method for a two-dimensional fracture problem ⋮ An optimal finite element method with Uzawa iteration for Stokes equations including corner singularities ⋮ Block method for problems on L-shaped domains ⋮ An Accurate Singular Boundary Element for Two-Dimensional Problems in Potential Theory with Corner Singularities ⋮ Highly accurate solutions of Motz's and the cracked beam problems ⋮ Solving Laplacian problems with boundary singularities: a comparison of a singular function boundary integral method with the \(p\)/\(hp\) version of the finite element method

Cites Work

• Unnamed Item
• An efficient finite element method for treating singularities in Laplace's equation
• An efficient method for subtracting off singularities at corners for Laplace's equation
• Boundary Methods for Solving Elliptic Problems with Singularities and Interfaces
• The integrated singular basis function method for the stick‐slip and the die‐swell problems
• On grid refinement at point singularities forh-p methods
• A comparison of adaptive refinement techniques for elliptic problems

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