Contribution to the treatment of constraints due to standard boundary conditions in the context of the mixed Web-spline finite element method

This article proposes a new boundary condition using the web-spline that is formulated for a finite element space approximation. It enables to remedy the problems of constraints due to homogeneous and non-homogeneous Dirichlet boundary conditions. The 2D linear Navier- Lame elasticity equation with the condition CA,B is considered, which allows total insertion of the essential boundary conditions into the linear system obtained without the use of a numerical method such as the Lagrange multiplier. This development proposal of a mixed finite element method using B-splines Web-spline space offers an exact implementation of the homogeneous Dirichlet boundary conditions and eliminate the constraints imposed by the standard conditions. This offers proof of the existence and uniqueness of the weak solution, as well as convergence of the numerical solution for the quadratic case. The weighted extended B-spline approach is thus seen to offer a more practical solution.