A mixed finite element method for nearly incompressible elasticity and Stokes equations using primal and dual meshes with quadrilateral and hexahedral grids. (English) Zbl 1293.65157
Summary: We consider a mixed finite element method for approximating the solution of nearly incompressible elasticity and Stokes equations. The finite element method is based on quadrilateral and hexahedral triangulation using primal and dual meshes. We use the standard bilinear and trilinear finite element space enriched with element-wise defined bubble functions with respect to the primal mesh for the displacement or velocity, whereas the pressure space is discretized by using a piecewise constant finite element space with respect to the dual mesh.
MSC:
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65N15 | Error bounds for boundary value problems involving PDEs |
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 74B10 | Linear elasticity with initial stresses |
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 76D07 | Stokes and related (Oseen, etc.) flows |
Keywords:
mixed finite elements; nearly incompressible elasticity; primal and dual meshes; Stokes equations; inf-sup conditionReferences:
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