The lowest-order weak Galerkin finite element method for the Darcy equation on quadrilateral and hybrid meshes

JOURNAL OF COMPUTATIONAL PHYSICS

卷:359

Article

Liu, Jiangguo¹  Tavener, Simon¹  Wang, Zhuoran¹ 

[1] Colorado State Univ, Dept Math, Ft Collins, CO 80523 USA

关键词: Darcy flow;    Hybrid meshes;    Lowest order finite elements;    Quadrilateral meshes;    Weak Galerkin;   

DOI  :  10.1016/j.jcp.2018.01.001

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free