A direct block sparse solution of the mixed finite element equations

Abstract

In this paper a practical procedure for the solution of really sized mixed problems, generating a continuous stress field (where appropriate) and having both the stress and displacement boundary conditions exactly satisfied, is described. The system matrix for the present formulation can be subdivided into the blocks, if the field variables (stresses and displacements) are separated for computational purposes. In addition, the structure of these blocks is sparse, similarly as the structure of the stiffness matrix in classical finite element analysis. Block sparse solution procedure, accounting for the pattern of the resulting system matrix is proposed. Computer implementation confirmed feasibility of the described solution procedure. In addition, numerical tests show remarkably high accuracy and convergence rate of the present mixed scheme for both the stresses and displacements. Due to high accuracy of the scheme, it can be competitive in comparison with usual displacement approach, although the count of arithmetic operations for the same mesh density in mixed procedure can be an order of magnitude larger than in classical finite element analysis.