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.
Conservative P1 conforming and nonconforming galerkin fems: Effective flux evaluation via a nonmixed method approach.SIAM Journal on Numerical Analysis, 38(2):660–680
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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.