Γ-convergence of external approximations in boundary value problems involving the bi-Laplacian
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 9th International Congress on computational and applied mathematics
Journal of Scientific Computing
| Hi-index | 0.00 |
In this work we present a finite element method for the biharmonic problem based on the primal mixed formulation of Ciarlet and Raviart [A mixed finite element method for the biharmonic equation, in Symposium on Mathematical Aspects of Finite Elements in Partial Differential Equations, C. de Boor, ed., Academic Press, New York, 1974, pp. 125--143]. We introduce a dual mesh and a suitable approximation of the constraint that enables us to eliminate the auxiliary variable with no computational effort. Thus, the discrete problem turns to be governed by a system of linear equations with symmetric and positive definite coefficients and can be solved by classical algorithms. The construction of the stiffness matrix is obtained by using Courant triangles and can be done with great efficiency.