Solving the Problem of Constraints Due to Dirichlet Boundary Conditions in the Context of the Mini Element Method

Abstract

In this work, we propose a new boundary condition called CA;B to remedy the problems of constraints due to the Dirichlet boundary conditions. We consider the 2D-linear elasticity equation of Navier-Lam´e with the condition CA;B. The latter allows to have a total insertion of the essential boundary condition in the linear system obtained without going through a numerical method like the lagrange multiplier method, this resulted in a non-extended linear system easy to reverse. We have developed the mixed finite element method using the mini element space (P1 + bubble, P1). Finally we have shown the efficiency and the feasibility of the limited condition CA;B.