A mass-conservative characteristic splitting mixed finite element method for convection-dominated Sobolev equation

Jiansong Zhang, Yuezhi Zhang, Hui Guo and Hongfei Fu

Mathematics and Computers in Simulation (MATCOM), 2019, vol. 160, issue C, 180-191

Abstract: In this article, a new characteristic splitting mixed finite element method is proposed for solving convection-dominated Sobolev equation. In this algorithm the mass-conservative characteristic (MCC) scheme is applied to approximate the time derivative term plus the convection term, and the splitting mixed finite element (SMFE) technique is used to approximate the primal unknown function and the introduced unknown flux. This procedure not only keeps the mass balance but also results in a splitting symmetric positive definite mixed system where we do not need to solve a coupled system. The convergence analysis is considered and the corresponding optimal error estimates in L2 norm for the primal unknown and in H(div) norm for the unknown flux are derived, respectively. Numerical examples are provided to confirm the theoretical results.

Keywords: Mass-conservative; The method of characteristics; Splitting system; Mixed element; Sobolev equation (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:160:y:2019:i:c:p:180-191

DOI: 10.1016/j.matcom.2018.12.016

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