Elasticity With Mixed Finite Element

Abstract

In this article we are intending to solve the Navier-Lame problem in 2D with Dirichlet and Neumann boundaries, using the mixed finite element P 1 -bubble P 1 . We want to introduce a new weak formulation of this problem with help of another new unknown which is equal to divergence of the displacement. We do the necessary calculations of this problem in order to come up with a Matlab program that visualizes the numerical solution.Some numerical results which are shown, prove that our method is more efficient than the ordinary finite element.

WEB-Spline Finite Elements for the Approximation of Navier-Lamé System with CA,B Boundary Condition

“…The finite element method has become the method of choice for solving many types of partial differential equations in engineering and physical sciences. Important applications include structural mechanics, fluid flow, thermodynamics, and electromagnetic fields [1], using the approximation of Lagrange [2]. This type of approximation has experienced a great restriction in the level of the geometric domain, especially in the case of complicated boundaries such as that in the form of curvilinear graphs.…”