A Fully Computable A Posteriori Error Estimate for the Stokes Equations on Polytopal Meshes

Journal Article · Tue Jan 01 04:00:00 EST 2019 · SIAM Journal on Numerical Analysis

DOI:https://doi.org/10.1137/18M1171515· OSTI ID:1531205

Bao, Feng ^[1]; Mu, Lin ^[2]; Wang, Jin ^[3]

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1. Florida State Univ., Tallahassee, FL (United States). Dept. of Mathematics
2. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Computer Science and Mathematics Division
3. Univ. of Tennessee, Chattanooga, TN (United States)

Here in this paper, we present a simple a posteriori error estimate for the weak Galerkin finite element method for the Stokes equation. This residual type estimator can be applied to general meshes such as polytopal mesh or meshes with hanging nodes. The reliability and efficiency of the estimator are proved in this paper. Five numerical tests demonstrate the effectiveness and flexibility of the adaptive mesh refinement guided by the designed error estimator.

• Research Organization: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
• Sponsoring Organization: USDOE
• Grant/Contract Number: AC05-00OR22725
• OSTI ID: 1531205
• Journal Information: SIAM Journal on Numerical Analysis, Journal Name: SIAM Journal on Numerical Analysis Journal Issue: 1 Vol. 57; ISSN 0036-1429
• Publisher: Society for Industrial and Applied Mathematics
• Country of Publication: United States
• Language: English

Related Subjects

finite element methods
97 MATHEMATICS AND COMPUTING
Stokes equations
a posterior error estimate
polytopal meshes
weak Galerkin