Interior energy error estimates for the weak Galerkin finite element method

Li, Hengguang; Mu, Lin; Ye, Xiu

doi:10.1007/s00211-017-0940-4

Interior energy error estimates for the weak Galerkin finite element method

Journal Article · Wed Dec 20 04:00:00 EST 2017 · Numerische Mathematik

DOI:https://doi.org/10.1007/s00211-017-0940-4· OSTI ID:1415199

Li, Hengguang ^[1]; ^[2]; Ye, Xiu ^[3]

Wayne State Univ., Detroit, MI (United States). Department of Mathematics
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Computer Science and Mathematics Division
University of Arkansas, Little Rock, AR (United States). Department of Mathematics

Consider the Poisson equation in a polytopal domain ΩRC^d (d=2,3) as the model problem. In this paper, we study interior energy error estimates for the weak Galerkin finite element approximation to elliptic boundary value problems. In particular, we show that the interior error in the energy norm is bounded by three components: the best local approximation error, the error in negative norms, and the trace error on the element boundaries. This implies that the interior convergence rate can be polluted by solution singularities on the domain boundary, even when the solution is smooth in the interior region. Numerical results are reported to support the theoretical findings. Lastly, to the best of our knowledge, this is the first local energy error analysis that applies to general meshes consisting of polytopal elements and hanging nodes.

Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)

DOE Contract Number:: AC05-00OR22725

OSTI ID:: 1415199

Journal Information:: Numerische Mathematik, Journal Name: Numerische Mathematik Journal Issue: 2 Vol. 139; ISSN 0029-599X

Publisher:: Springer Berlin Heidelberg

Country of Publication:: United States

Language:: English

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Interior energy error estimates for the weak Galerkin finite element method

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