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An a posteriori error estimator for a LPS method for Navier-Stokes equations. (English) Zbl 1425.76126

Summary: In this work we develop an a posteriori error estimator, of the hierarchical type, for the Local Projection Stabilized (LPS) finite element method introduced in [the first author et al., IMA J. Numer. Anal. 36, No. 1, 267–295 (2016; Zbl 1425.76125)], applied to the incompressible Navier-Stokes equations. The technique uses the solution of locals problems posed on appropriate finite dimensional spaces of bubble-like functions, to approach the error. Several numerical tests confirm the theoretical properties of the estimator and its performance.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs

Citations:

Zbl 1425.76125
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References:

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