A Galerkin boundary node method and its convergence analysis. (English) Zbl 1189.65291

Li, Xiaolin; Zhu, Jialin

J. Comput. Appl. Math. 230, No. 1, 314-328 (2009).

The paper is concerned with a new Galerkin boundary node method for solving boundary value problems in \({\mathbb R}^2\). The method is based on a variational form of the boundary integral formulation of the problem. Trial and test functions are generated by the moving least-square approximation leading to a meshless boundary type method. Unlike the original boundary node method, the proposed one generates symmetric matrices for symmetric problems and implements the boundary conditions accurately since they are enforced by the variational formulation. Error estimates are provided for the Dirichlet problem of the Laplace equation. Some numerical tests are given to illustrate the theoretical error estimates.

Reviewer: Ana M. Alonso Rodriguez (Povo)

MSC:

65N38	Boundary element methods for boundary value problems involving PDEs
65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12	Stability and convergence of numerical methods for boundary value problems involving PDEs
65N15	Error bounds for boundary value problems involving PDEs
35J05	Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation

Keywords:

Galerkin boundary node method; moving least-squares; meshless methods; convergence; boundary element method; numerical examples; error estimates

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