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A Cartesian grid embedded boundary method for Poisson’s equation on irregular domains. (English) Zbl 0923.65079
The authors present a finite-volume method for the Poisson equation on a curved planar region covered by a regular grid. A special discretization is used on computational cells which extend beyond the domain. It is shown that the method is second-order accurate, and numerical examples suggest that the condition number of the matrix is bounded independent of the fact that the intersection of some computational cells with the domain may be very small.

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
Full Text: DOI
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