A PRIORI L2 ERROR ANALYSIS FOR AN EXPANDED MIXED FINITE ELEMENT METHOD FOR QUASILINEAR PSEUDO-PARABOLIC EQUATIONS

Title & Authors
A PRIORI L2 ERROR ANALYSIS FOR AN EXPANDED MIXED FINITE ELEMENT METHOD FOR QUASILINEAR PSEUDO-PARABOLIC EQUATIONS
Ohm, Mi Ray; Lee, Hyun Young; Shin, Jun Yong;

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