Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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A PRIORI L2 ERROR ANALYSIS FOR AN EXPANDED MIXED FINITE ELEMENT METHOD FOR QUASILINEAR PSEUDO-PARABOLIC EQUATIONS

  • Ohm, Mi Ray (Division of Information Systems Engineering Dongseo University) ;
  • Lee, Hyun Young (Department of Mathematics Kyungsung University) ;
  • Shin, Jun Yong (Department of Applied Mathematics Pukyong National University)
  • Received : 2012.09.18
  • Published : 2014.01.01
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Abstract

Based on an expanded mixed finite element method, we consider the semidiscrete approximations of the solution u of the quasilinear pseudo-parabolic equation defined on ${\Omega}{\subset}R^d$, $1{\leq}d{\leq}3$. We construct the semidiscrete approximations of ${\nabla}u$ and $a(u){\nabla}u+b(u){\nabla}u_t$ as well as u and prove the existence of the semidiscrete approximations. And also we prove the optimal convergence of ${\nabla}u$ and $a(u){\nabla}u+b(u){\nabla}u_t$ as well as u in $L^2$ normed space.

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Acknowledgement

Supported by : Dongseo University

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