The error of the reduced solution for elliptic interface problems is controlled entirely by the approximation error of the interface data, recovering the full solution to roundoff accuracy once the interface is accurate.
An accurateH(div) flux reconstruction for discontinuous galerkin approximations of elliptic problems.Comptes Rendus Math´ ematique, 345(12):709–712
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Interface Reduction for Elliptic Interface Problems with Conservative Flux Reconstruction
The error of the reduced solution for elliptic interface problems is controlled entirely by the approximation error of the interface data, recovering the full solution to roundoff accuracy once the interface is accurate.