Convergence analysis of a symmetric dual-wind discontinuous Galerkin method for a parabolic variational inequality
Convergence analysis of a symmetric dual-wind discontinuous Galerkin method for a parabolic variational inequality
复制标题
抛物型变分不等式的对称双风间断伽辽金法的收敛性分析
DOI：
10.1016/j.cam.2022.114922
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发表时间：
2023
影响因子：
2.4
通讯作者：
Zhang, Yi
中科院分区：
文献类型：
--
作者：
Boyana, Satyajith Bommana;Lewis, Thomas;Rapp, Aaron;Zhang, Yi
研究了求解抛物型变分不等式的对称双风不连续伽辽金方法。通过空间上的对称双风DG离散和时间上的倒向欧拉离散，提出了一种求解时变障碍问题的全离散方案。在精确解的合理正则性假设下，通过引入一种新的插值算子，即标准插值算子和正保插值算子的组合，证明了数值解在L∞(l2)和l2 （h1）类能量误差下的收敛性。数值实验验证了该方法的有效性。
This paper investigates a symmetric dual-wind discontinuous Galerkin (DG) method for solving parabolic variational inequalities. By employing a symmetric dual-wind DG discretization in space and a backward Euler discretization in time, we propose a fully discrete scheme to solve a time-dependent obstacle problem. Under reasonable regularity assumptions on the exact solution, we prove the convergence of numerical solutions with rates in the L∞(L 2) and L 2 (H 1)-like energy errors by introducing a new interpolation operator which is a combination of the standard interpolation operator and a positive-preserving interpolation operator. Numerical experiments are provided to validate the effectiveness of the proposed method.