A Posteriori Error Estimates for a Modified Weak Galerkin Finite Element Approximation of Second Order Elliptic Problems with DG Norm (Journal of Computational Mathematics, 2021)
In this paper, we derive a residual based a posteriori error estimator for a modifiedweak Galerkin formulation of second order elliptic problems. We prove that the errorestimator used for interior penalty discontinuous Galerkin methods still gives both upperand lower bounds for the modified weak Galerkin method, though they have essentiallydifferent bilinear forms. More precisely, we prove its reliability and efficiency for the actualerror measured in the standard DG norm. We further provide an improved a priori errorestimate under minimal regularity assumptions on the exact solution. Numerical resultsare presented to verify the theoretical analysis.
Keywords: Modified weak Galerkin method; A posteriori error estimate; A medius error analysis.