A SPLIT LEAST-SQUARES CHARACTERISTIC MIXED FINITE ELEMENT METHOD FOR THE CONVECTION DOMINATED SOBOLEV EQUATIONS

- Journal title : Journal of applied mathematics & informatics
- Volume 34, Issue 1_2, 2016, pp.19-34
- Publisher : The Korean Society of Computational and Applied Mathematics
- DOI : 10.14317/jami.2016.019

Title & Authors

A SPLIT LEAST-SQUARES CHARACTERISTIC MIXED FINITE ELEMENT METHOD FOR THE CONVECTION DOMINATED SOBOLEV EQUATIONS

OHM, MI RAY; SHIN, JUN YONG;

OHM, MI RAY; SHIN, JUN YONG;

Abstract

In this paper, we present a split least-squares characteristic mixed finite element method(MFEM) to get the approximate solutions of the convection dominated Sobolev equations. First, to manage both convection term and time derivative term efficiently, we apply a least-squares characteristic MFEM to get the system of equations in the primal unknown and the flux unknown. Then, we obtain a split least-squares characteristic MFEM to convert the coupled system in two unknowns derived from the least-squares characteristic MFEM into two uncoupled systems in the unknowns. We theoretically prove that the approximations constructed by the split least-squares characteristic MFEM converge with the optimal order in L^{2} and H^{1} normed spaces for the primal unknown and with the optimal order in L^{2} normed space for the flux unknown. And we provide some numerical results to confirm the validity of our theoretical results.

Keywords

Convection dominated Sobolev equations;A split least-squares method;characteristic mixed finite element method;convergence of optimal order;

Language

English

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