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Exponential convergence of mixed \(hp\)-DGFEM for Stokes flow in polygons. (English) Zbl 1130.76331
Summary: We analyze mixed \(hp\)-discontinuous Galerkin finite element methods (DGFEM) for Stokes flow in polygonal domains. In conjunction with geometrically refined quadrilateral meshes and linearly increasing approximation orders, we prove that the \(hp\)-DGFEM leads to exponential rates of convergence for piecewise analytic solutions exhibiting singularities near corners.

MSC:
76D07 Stokes and related (Oseen, etc.) flows
76M10 Finite element methods applied to problems in fluid mechanics
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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