Mixed methods using standard conforming finite elements

doi:10.1016/j.cma.2008.10.002

Return

Mixed methods using standard conforming finite elements

2009-01-01

PRE

Jichun Li *

Todd Arbogast

Yunqing Huang

DOI：10.1016/j.cma.2008.10.002

Original

Original request for help

Save

Abstract

En 中文

We investigate the mixed finite element method (MFEM) for solving a second order elliptic problem with a lowest order term, as might arise in the simulation of single-phase flow in porous media. We find that traditional mixed finite element spaces are not necessary when a positive lowest order (i.e., reaction) term is present. Hence, we propose to use standard conforming finite elements Q(k) x (Q(k))(d) on rectangles or P(k) x (P(k))(d) on simplices to solve for both the pressure and velocity field in d dimensions. The price we pay is that we have only sub-optimal order error estimates. With a delicate superconvergence analysis, we find some improvement for the simplest pair Q(k) x (Q(k))(d) with any k >= 1, or for P(1) x (P(1))(d), when the mesh is uniform and the solution has one extra order of regularity. We also prove similar results for both parabolic and second order hyperbolic problems. Numerical results using Q(1) x (Q(1))(2) and P(1) x (P(1))(2) are presented in support of our analysis. These observations allow us to simplify the implementation of the MFEM, especially for higher order approximations, as might arise in an hp-adaptive procedure. (C) 2008 Elsevier B.V. All rights reserved.

Keywords:

Mixed finite element

Elliptic

Parabolic

Hyperbolic

Inf-sup condition

AI Summary

Key information extracted from the uploaded paper, including a brief overview, abstract, background, key highlights, visual analysis, and future outlook.