A priori error estimates of P20-P1 mixed finite element methods for a class of nonlinear parabolic equations
Ch. Liu1, T. Hou2, Zh. Weng3
1Hunan University of Science and Engineering, Yongzhou, China
2Beihua University, Jilin, China
3Huaqiao University, Quanzhou, China
Keywords: nonlinear parabolic equations, P-P mixed finite element method, a priori error estimates, square integrable function space
Abstract
In this paper, we consider P 20- P 1 mixed finite element approximations of a class of nonlinear parabolic equations. The backward Euler scheme for temporal discretization is used. Firstly, a new mixed projection is defined and the related a priori error estimates are proved. Secondly, optimal a priori error estimates for pressure variable and velocity variable are derived. Finally, a numerical example is presented to verify the theoretical results.
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