Discrete mass conservation for porous media saturated flow

Document Type

Article

Publication Date

3-1-2014

Department

Department of Mathematical Sciences

Abstract

Global and local mass conservation for velocity fields associated with saturated porous media flow have long been recognized as integral components of any numerical scheme attempting to simulate these flows. In this work, we study finite element discretizations for saturated porous media flow that use Taylor-Hood (TH) and Scott-Vogelius (SV) finite elements. The governing equations are modified to include a stabilization term when using the TH elements, and we provide a theoretical result that shows convergence (with respect to the stabilization parameter) to pointwise mass-conservative solutions. We also provide results using the SV approximation pair. These elements are pointwise divergence free, leading to optimal convergence rates and numerical solutions. We give numerical results to verify our theory and a comparison with standard mixed methods for saturated flow problems.

Publisher's Statement

Copyright © 2013 Wiley Periodicals, Inc. Publisher’s version of record: https://doi.org/10.1002/num.21831

Publication Title

Numerical Methods for Partial Differential Equations

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