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首页> 外文期刊>Journal of Computational Physics >The lowest-order weak Galerkin finite element method for the Darcy equation on quadrilateral and hybrid meshes
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The lowest-order weak Galerkin finite element method for the Darcy equation on quadrilateral and hybrid meshes

机译：四边形和杂交网上Darcy方程的最低级弱Galerkin有限元方法

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This paper investigates the lowest-order weak Galerkin finite element method for solving the Darcy equation on quadrilateral and hybrid meshes consisting of quadrilaterals and triangles. In this approach, the pressure is approximated by constants in element interiors and on edges. The discrete weak gradients of these constant basis functions are specified in local Raviart-Thomas spaces, specifically RT0 for triangles and unmapped RT[0] for quadrilaterals. These discrete weak gradients are used to approximate the classical gradient when solving the Darcy equation. The method produces continuous normal fluxes and is locally mass-conservative, regardless of mesh quality, and has optimal order convergence in pressure, velocity, and normal flux, when the quadrilaterals are asymptotically parallelograms. Implementation is straightforward and results in symmetric positive-definite discrete linear systems. We present numerical experiments and comparisons with other existing methods. (C) 2018 Elsevier Inc. All rights reserved.
机译：本文研究了求解四边形和三角形组成的四边形和混合网上达西方程的最低秩序弱Galerkin有限元方法。在这种方法中，压力由元件内部和边缘的常数近似。这些常量基本函数的离散弱梯度在本地Raviart-Thomas空间中指定，特别是RT0用于三角形，对于四边形的RT0 [0]。这些离散的弱梯度用于在求解达西方程时近似经典梯度。该方法产生连续的正常助熔剂，并且是局部质量保守的，无论网格质量如何，当四边形都是渐近平行四边形时，具有最佳的网状质量，并且在压力，速度和正常通量方面具有最佳的订单会聚。实施是简单的，结果是对称的正面定义离散线性系统。我们呈现了与其他现有方法的数值实验和比较。 （c）2018年Elsevier Inc.保留所有权利。

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