Application of tensor analysis to the finite element method

This paper presents the application of tensor analysis to the finite element (FE) method. A FE formulation is presented where the suffix notation and the Einstein's convention are used instead of the matrix algebra notation. The usage of the proposed notation avoids the drawbacks of matrix algebra and allows the easy implementation of the FE method in a computer code. The Dirichlet boundary condition is included in the FE formulation through the use of suffix constraints. Afterwards, the suffix notation is applied to the FE formulation of the Poisson equation and it is implemented in a C language. Finally, two numerical examples are solved to illustrate the advantages of using the proposed notation in the FE method.