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A posteriori error estimation in finite element analysis. (English) Zbl 0895.76040

Summary: This monograph presents a summary account of the subject of a posteriori error estimation for finite element approximations of problems in mechanics. The study primarily focuses on methods for linear elliptic boundary value problems. However, error estimation for unsymmetrical systems, nonlinear problems, including the Navier-Stokes equations, and indefinite problems, such as represented by the Stokes problem, are included. The main thrust is to obtain error estimators for the error measured in the energy norm, but techniques for other norms are also discussed.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76D07 Stokes and related (Oseen, etc.) flows
76D05 Navier-Stokes equations for incompressible viscous fluids
65N15 Error bounds for boundary value problems involving PDEs
76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
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