Continuous/discontinuous Galerkin methods stabilized through transfer functions applied to the incompressible elasticity and to the Stokes problem. (English) Zbl 1423.74878
Summary: In this work, we present a family of new Continuous/Discontinuous mixed formulations with interpolation of equal order for velocity and pressure for the Stokes problem and incompressible elasticity. The degrees of freedom associated to the discontinuous component are eliminated and an approach with computational effort similar to that of the continuous formulation is obtained. An analysis of continuity and weak coercivity (InfSup condition) is performed and it is proved that the formulation is continuous and satisfies the InfSup condition on an appropriated norm. Error estimates, derived from theorems and the lemma presented are obtained on a similar norm to the one of the GLS method. Numerical experiments with the cavity problem and a smooth solution problem show the robustness of the new formulation.
MSC:
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 74B05 | Classical linear elasticity |
| 74G15 | Numerical approximation of solutions of equilibrium problems in solid mechanics |
| 76D07 | Stokes and related (Oseen, etc.) flows |
Keywords:
continuous Galerkin; discontinuous Galerkin; continuous-discontinuous Galerkin; Stokes problem; incompressible elasticityReferences:
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