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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.

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
Full Text: DOI
[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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