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Weak-Galerkin finite element methods for a second-order elliptic variational inequality

机译：二阶椭圆变分不等式的弱Galerkin有限元方法

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A weak-Galerkin finite element method is used to determine approximate solutions of an elliptic variational inequality. Three sets of basis functions are employed: the first has constant values inside each element and on each edge; the second has constant values inside each element but is a linear polynomial on each edge; and the third has linear polynomials inside each element and on each edge. Error estimates, including convergence rates, are derived for all three cases. Numerical results were provided to illustrate the theoretical results, to show that the choice of how the obstacle function is approximated affects those rates, and to show the super-convergence for piecewise constant basis functions. (C) 2018 Elsevier B.V. All rights reserved.
机译：弱Galerkin有限元方法用于确定椭圆变分不等式的近似解。采用了三组基函数：第一组在每个元素内部和每个边上具有常数。第二个在每个元素内部具有恒定值，但在每个边上都是线性多项式；第三个在每个元素内部和每个边上都有线性多项式。对所有三种情况都得出包括收敛速度在内的误差估计。提供了数值结果以说明理论结果，以表明如何近似选择障碍函数会影响这些比率，并显示分段常数基函数的超收敛性。 （C）2018 Elsevier B.V.保留所有权利。

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