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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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A weak Galerkin mixed finite element method for second order elliptic problems
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by Junping Wang and Xiu Ye PDF
Math. Comp. 83 (2014), 2101-2126 Request permission

Abstract:

A new weak Galerkin (WG) method is introduced and analyzed for the second order elliptic equation formulated as a system of two first order linear equations. This method, called WG-MFEM, is designed by using discontinuous piecewise polynomials on finite element partitions with arbitrary shape of polygons/polyhedra. The WG-MFEM is capable of providing very accurate numerical approximations for both the primary and flux variables. Allowing the use of discontinuous approximating functions on arbitrary shape of polygons/polyhedra makes the method highly flexible in practical computation. Optimal order error estimates in both discrete $H^1$ and $L^2$ norms are established for the corresponding weak Galerkin mixed finite element solutions.
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Additional Information
  • Junping Wang
  • Affiliation: Division of Mathematical Sciences, National Science Foundation, Arlington, Virginia 22230
  • MR Author ID: 216677
  • Email: jwang@nsf.gov
  • Xiu Ye
  • Affiliation: Department of Mathematics, University of Arkansas at Little Rock, Little Rock, Arkansas 72204
  • Email: xxye@ualr.edu
  • Received by editor(s): March 20, 2012
  • Received by editor(s) in revised form: November 23, 2012, and December 11, 2012
  • Published electronically: May 5, 2014
  • Additional Notes: The research of the first author was supported by the NSF IR/D program, while working at the 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
    This research was supported in part by National Science Foundation Grant DMS-1115097
  • © Copyright 2014 American Mathematical Society
  • Journal: Math. Comp. 83 (2014), 2101-2126
  • MSC (2010): Primary 65N15, 65N30, 76D07; Secondary 35B45, 35J50
  • DOI: https://doi.org/10.1090/S0025-5718-2014-02852-4
  • MathSciNet review: 3223326