OPTIMAL L2-ERROR ESTIMATES FOR EXPANDED MIXED FINITE ELEMENT METHODS OF SEMILINEAR SOBOLEV EQUATIONS

Title & Authors
OPTIMAL L2-ERROR ESTIMATES FOR EXPANDED MIXED FINITE ELEMENT METHODS OF SEMILINEAR SOBOLEV EQUATIONS
Ohm, Mi Ray; Lee, Hyun Young; Shin, Jun Yong;

Abstract
In this paper we derive a priori $\small{L^{\infty}(L^2)}$ error estimates for expanded mixed finite element formulations of semilinear Sobolev equations. This formulation expands the standard mixed formulation in the sense that three variables, the scalar unknown, the gradient and the flux are explicitly treated. Based on this method we construct finite element semidiscrete approximations and fully discrete approximations of the semilinear Sobolev equations. We prove the existence of semidiscrete approximations of u, $\small{-{\nabla}u}$ and $\small{-{\nabla}u-{\nabla}u_t}$ and obtain the optimal order error estimates in the $\small{L^{\infty}(L^2)}$ norm. And also we construct the fully discrete approximations and analyze the optimal convergence of the approximations in $\small{{\ell}^{\infty}(L^2)}$ norm. Finally we also provide the computational results.
Keywords
semilinear Sobolev equations;expanded mixed finite element method;semidiscrete approximations;fully discrete approximations;computational results;
Language
English
Cited by
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