A diffuse interface box method for elliptic problems

01/27/2021

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by   G. Negrini, et al.

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We introduce a diffuse interface box method (DIBM) for the numerical approximation on complex geometries of elliptic problems with Dirichlet boundary conditions. We derive a priori H^1 and L^2 error estimates highlighting the rôle of the mesh discretization parameter and of the diffuse interface width. Finally, we present a numerical result assessing the theoretical findings.