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首页> 外文期刊>Applied numerical mathematics >Error estimates in weak Galerkin finite element methods for parabolic equations under low regularity assumptions
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Error estimates in weak Galerkin finite element methods for parabolic equations under low regularity assumptions

机译：低规律假设下抛物方程弱Galerkin有限元方法的误差估计

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摘要

In this paper, we consider the weak Galerkin finite element approximations of second order linear parabolic problems in two dimensional convex polygonal domains under the low regularities of the solutions. Optimal order error estimates in L~2(L~2) and L~2(H~1) norms are shown to hold for both the spatially discrete continuous time and the discrete time weak Galerkin finite element schemes, which allow using the discontinuous piecewise polynomials on finite element partitions with the arbitrary shape of polygons with certain shape regularity. The fully discrete scheme is based on first order in time Euler method. We have derived O(h~(r+1)) in L~2(L~2) norm and O(h~r) in L~2(H~1) norm when the exact solution u ∈ L~2(O. T; H~(r+1)(Ω))∩H~1 (0, T; H~(r-1)(Ω)), for some r≥ 1. Numerical experiments are reported for several test cases to justify our theoretical convergence results.
机译：在本文中，我们考虑在解决方案的低规律下二维凸多边形域中二阶线性抛物面问题的弱Galerkin有限元近似。 L〜2（L〜2）和L〜2（H〜1）规范中的最佳订单误差估计显示为空间离散的连续时间和离散时间弱Galerkin有限元件方案，允许使用不连续分段具有特定形状规律的多边形任意形状的有限元分隔膜的多项式。完全离散方案基于时间欧拉方法的一阶。当精确的解决方案U≠L〜2时，我们在L〜2（L〜2）规范中，在L〜2（L〜2）规范中，在L〜2（H〜1）规范中（H〜1）规范（ O. T; H〜（R + 1）（ω））∩H〜1（0，T; H〜（R-1）（ω）），对于一些R≥1.数值实验据报道了几种测试用例证明我们的理论融合结果。

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