A Finite-Element Method for Laplace- and Helmholtz-Type Boundary Value Problems with Singularities

Authors:
Xiaonan Wu;Houde Han
Affiliations:
-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
1997

Citing 0
Cited 6

The singular finite element method for some elliptic boundary value problem with interface

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A high-order integral algorithm for highly singular PDE solutions in Lipschitz domains

Computing
Error estimates of the finite element method for the exterior Helmholtz problem with a modified DtN boundary condition

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Coupling of Dirichlet-to-Neumann boundary condition and finite difference methods in curvilinear coordinates for multiple scattering

Journal of Computational Physics
Singularities and treatments of elliptic boundary value problems

Mathematical and Computer Modelling: An International Journal
The highly accurate block-grid method in solving Laplace's equation for nonanalytic boundary condition with corner singularity

Computers & Mathematics with Applications

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Abstract

Laplace- and Helmholtz-type boundary value problems with singularities are considered. A sequence of approximations to the exact boundary conditions at an artificial boundary is given. Then the original problem is reduced to a boundary value problem in a domain away from the singularities. Furthermore, finite-element approximations are applied to this problem and error estimates are obtained. Finally, some numerical examples show the effectiveness of this method.