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arXiv · 1804.03998

Superconvergence of the Gradient Approximation for Weak Galerkin Finite Element Methods on Nonuniform Rectangular Partitions

Dan Li·Chunmei Wang·Junping Wang
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Abstract

This article presents a superconvergence for the gradient approximation of the second order elliptic equation discretized by the weak Galerkin finite element methods on nonuniform rectangular partitions. The result shows a convergence of ${\cal O}(h^r)$, $1.5\leq r \leq 2$, for the numerical gradient obtained from the lowest order weak Galerkin element consisting of piecewise linear and constant functions. For this numerical scheme, the optimal order of error estimate is ${\cal O}(h)$ for the gradient approximation. The superconvergence reveals a superior performance of the weak Galerkin finite element methods. Some computational results are included to numerically validate the superconvergence theory.

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Dan Li, Chunmei Wang, Junping Wang. 2018-04-11. Superconvergence of the Gradient Approximation for Weak Galerkin Finite Element Methods on Nonuniform Rectangular Partitions. https://arxiv.org/abs/1804.03998

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