Title

Continuous Mixed Finite Element for the Second Order Elliptic Equation with a Low Order Term

Document Type

Article

Publication Date

3-9-2019

Publication Title

Journal of Computational and Applied Mathematics

Volume

357

First page number:

273

Last page number:

283

Abstract

We propose a mixed finite element, where the velocity (in terms of Darcy’s law) is approximated by the continuous Pk Lagrange elements and the pressure (the prime variable) is approximated by the discontinuous Pk−1 elements, for solving the second order elliptic equation with a low-order term. We show the quasi-optimality for this mixed finite element method. When a low order term is present, the traditional inf–sup condition is no longer required. But the inclusion condition, that the divergence of the discrete velocity space is a subspace of the discrete pressure space, is required. Thus the Taylor–Hood element and most other continuous-pressure mixed elements do not converge. Numerical tests are provided on the new elements and most other popular mixed elements.

Keywords

Continuous mixed finite element; Triangular grid; Tetrahedral grid

Disciplines

Applied Mathematics

Language

English

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