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http://dx.doi.org/10.4134/JKMS.2014.51.1.067

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)
Publication Information
Journal of the Korean Mathematical Society / v.51, no.1, 2014 , pp. 67-86 More about this Journal
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.
Keywords
pseudo-parabolic equation; an expanded mixed finite element method; semidiscrete approximations; $L^2$ optimal convergence;
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