An analysis of the weak Galerkin finite element method for convection–diffusion equations

Tie Zhang and Yanli Chen

Applied Mathematics and Computation, 2019, vol. 346, issue C, 612-621

Abstract: We study the weak finite element method solving convection–diffusion equations. A new weak finite element scheme is presented based on a special variational form. The optimal order error estimates are derived in the discrete H1-norm, the L2-norm and the L∞-norm, respectively. In particular, the H1-superconvergence of order k+2 is obtained under certain condition if polynomial pair Pk(K)×Pk+1(∂K) is used in the weak finite element space. Finally, numerical examples are provided to illustrate our theoretical analysis.

Keywords: Weak Galerkin method; Optimal error estimate; Superconvergence; Convection–diffusion equation (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:346:y:2019:i:c:p:612-621

DOI: 10.1016/j.amc.2018.10.064

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