Penalty-Factor-Free Discontinuous Galerkin Methods for 2-Dim Stokes Problems

Authors:
Jiangguo Liu
Affiliations:
liu@math.colostate.edu
Venue:
SIAM Journal on Numerical Analysis
Year:
2011

Citing 11
Cited 1

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A Mixed Finite Element Method for the Stokes Equations Based on a Weakly Over-Penalized Symmetric Interior Penalty Approach

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Abstract

This paper presents two new finite element methods for two-dimensional Stokes problems. These methods are developed by relaxing the constraints of the Crouzeix-Raviart nonconforming $P_1$ finite elements. Penalty terms are introduced to compensate for lack of continuity or the divergence-free property. However, there is no need for choosing penalty factors, and the formulations are symmetric. These new methods are easy to implement and avoid solving saddle-point linear systems. Numerical experiments are presented to illustrate the proved optimal error estimates.