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| Paper IPM / M / 14522 |
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| Abstract: | |
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The purpose of this paper is to develop the element-free Galerkin method for a numerical simulation of the second order
elliptic equation with discontinuous coefficients. Discontinuities in the solution and in its normal derivatives
are prescribed on an interface inside the domain. The proposed method is one of the powerful meshless methods
based on moving least squares approximation. The element-free Galerkin method uses only a set of nodal points
to discretize the governing equation. No mesh in the classical sense is needed, but a background mesh is used
for integration purpose. A quadrilateral mesh unfitted with the interface is used for integration objective. The
Lagrange multipliers are used to enforce both Dirichlet boundary condition and Dirichlet jump condition. The
presented numerical experiments confirm the efficiency of the proposed method in comparison with some existing
methods for interface problems.
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