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The objective of this article is to discuss the existence and the uniqueness of a weighted extended B-spline- (WEB-spline-) based discrete solution for the 2D Navier-Lamé equation of linear elasticity with a different type of mixed boundary condition called CA,B boundary condition. Along with the usual weak mixed formulation, we give existence and uniqueness results for weak solution. Then, we illustrate the performance of Ritz–Galerkin schemes for a model problem and applications in linear elasticity. Finally, we discuss several implementation aspects. The numerical tests confirm that, due to the new integration routines, the weighted B-spline solvers have become considerably more efficient.

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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.