线性Sobolev方程的低次弱Galerkin有限元方法

A WEAK GALERKIN FINITE ELEMENT METHOD WITH POLYNOMIAL REDUCTION FOR LINEAR SOBOLEV EQUATIONS

低次弱Galerkin方法是在弱Galerkin方法的基础上给出了一个最优的有限元多项式空间{P_j(K),P_(j-1)(e),[P_(j-1)(K)]~2},并引进了一个稳定项,该方法在保持弱Galerkin方法精度的基础上减少了计算量.本文提出了线性Sobolev方程的半离散和全离散低次弱Galerkin有限元格式,建立了最优的L^2和|||·|||误差估计.

A weak Galerkin finite element merhod with polynomial reduction presents an optimal combination for the polynomial spaces {Pj （K）, Pj-1 （ e ）, [ Pj-1 （K） ]2 } and introduces a stabilizer term based on the weak Galerkin method.This method reduces the number of unknowns in the numerical scheme without compromising the accuracy of the numerical approximation. In this paper, the semi- didcrete and fully discrete weak Galerkin finite element schemes are propsed. Optimal order error estimates are established for the corresponding numerical approximations in both L2 and III · III norms.