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Energy norm a posteriori error estimation for mixed discontinuous Galerkin approximations of the Stokes problem. (English) Zbl 1065.76139
Summary: We develop a posteriori error estimation of mixed discontinuous Galerkin finite element approximations of Stokes problem. In particular, we derive computable upper bounds on the error, measured in terms of a natural (mesh-dependent) energy norm. This is done by rewriting the underlying method in a non-consistent form using appropriate lifting operators, and by employing a decomposition result for discontinuous spaces. Finally, we present a series of numerical experiments highlighting the performance of the proposed a posteriori error estimator on adaptively refined meshes.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76D07 Stokes and related (Oseen, etc.) flows
65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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[11] Girault, V., Rivière, B., and Wheeler, M. F. (2002). A Discontinuous Galerkin Method with Non-overlapping Domain Decomposition for the Stokes and Navier–Stokes problems, Technical Report 02-08, TICAM, UT Austin. In press in Math. Comp. · Zbl 1057.35029
[14] Houston, P., Perugia, I., and Schötzau, D. (2003). Energy Norm A Posteriori Error Estimation for Mixed Discontinuous Galerkin Approximations of the Maxwell Operator, Technical Report 2003-17, Department of Mathematics and Computer Science, University of Leicester. · Zbl 1063.78021
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