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A conservative particle approximation for a boundary advection-diffusion problem. (English) Zbl 0766.65095

The aim of this paper is to present and analyze a conservative two- dimensional extension of the deterministic method to the case of Dirichlet boundary conditions. The basic idea of the method is to add to the usual vorticity an extra term with support in a neighbourhood of the boundary. The boundary condition effects, as well as the diffusion effects, are taken into account by a modification of the weights of the particles. A boundary integral equation formulation is used to construct the method. The order of convergence of the method is of the same kind as in the caes of the whole space.
Reviewer: K.Zlateva (Russe)

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
35J25 Boundary value problems for second-order elliptic equations
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References:

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