Published

A posteriori error estimates for Weak Galerkin finite element methods for second order elliptic problems

Long Chen, Junping Wang, and Xiu Ye

Journal of Scientific Computing, 59(2), 496-511, 2014.

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ABSTRACT:

 A residual type a posteriori error estimator is presented and
analyzed for Weak Galerkin finite element methods for second order
elliptic problems. The error estimator is proved to be efficient and
reliable through two estimates, one from below and the other from
above, in terms of an $H^1$-equivalent norm for the exact error. Two
numerical experiments are conducted to demonstrate the effectiveness
of adaptive mesh refinement guided by this estimator.