A mixed finite element method based on a biorthogonal system for nearly incompressible elastic problems

Abstract

A Petrov--Galerkin scheme in a saddle point formulation gives rise to a non-symmetric saddle point problem. This article considers a non-symmetric saddle point problem with a penalty parameter. A mixed finite element method for linear elasticity based on a Petrov--Galerkin formulation is then analyzed within the framework of the non-symmetric saddle point problem with penalty. Working with a biorthogonal system to discretize the pressure equation, we obtain a robust and efficient numerical scheme for nearly incompressible linear elasticity using linear finite elements. A numerical example demonstrates the robustness of the approach. These results are useful to analyze a Petrov--Galerkin scheme in a saddle point problem. References

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