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A SPLIT LEAST-SQUARES CHARACTERISTIC MIXED FINITE ELEMENT METHOD FOR THE CONVECTION DOMINATED SOBOLEV EQUATIONS
A SPLIT LEAST-SQUARES CHARACTERISTIC MIXED FINITE ELEMENT METHOD FOR THE CONVECTION DOMINATED SOBOLEV EQUATIONS
Journal of applied mathematics & informatics. 2016. Jan, 34(1_2): 19-34
  • Received : August 08, 2015
  • Published : January 30, 2016
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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<sup>2</sup> and H<sup>1</sup> normed spaces for the primal unknown and with the optimal order in L<sup>2</sup> normed space for the flux unknown. And we provide some numerical results to confirm the validity of our theoretical results.
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