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On computing the pressure by the \(p\) version of the finite element method for Stokes problem. (English) Zbl 0741.76038

Summary: This paper introduces and analyzes two ways of extracting the hydrostatic pressure when solving Stokes problem using the \(p\) version of the finite element method. When one uses a local \(H^ 1\) projection, we show that optimal rates of convergence for the pressure approximation is achieved. When the pressure is not in \(H^ 1\), or the value of the pressure is only needed at a few points, one may extract the pressure pointwise using e.g. a single layer potential recovery. Negative, zero, and higher norm estimates for the Stokes velocity are derived within the framework of the \(p\) version of the F.E.M.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76D07 Stokes and related (Oseen, etc.) flows
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
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