Abstract
This article extends a recently developed superconvergence result for weak Galerkin (WG) approximations for modeling partial differential equations from constant coefficients to variable coefficients. This superconvergence features a rate that is two-order higher than the optimal-order error estimates in the usual energy and L2 norms. The extension from constant to variable coefficients for the modeling equations is highly non-trivial. The underlying technical analysis is based on the use of a sequence of projections and decompositions. Numerical results are presented to confirm the superconvergence theory for second-order elliptic problems with variable coefficients.
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Acknowledgements
Jun** Wang was supported by the National Science Foundation IR/D program, while working at National Science Foundation. However, any opinion, finding and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation. ** Wang
