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A fully computable a posteriori error estimate for the Stokes equations on polytopal meshes. (English) Zbl 1502.65176

Summary: 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.

MSC:

65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J50 Variational methods for elliptic systems
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
35Q35 PDEs in connection with fluid mechanics

Software:

PolyMesher
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Full Text: DOI

References:

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