Convergence analysis for an element-by-element finite element method Original Research Article

This paper describes an element-by-element iterative finite element algorithm for linear elasticity problems. While it does not claim to compete with conventional finite element solvers on a serial computer, it is very suitable for parallelization. It is constructed in a manner very similar to the Static Relaxation algorithm used in the Discrete Element Method, thus facilitating the development of a unified FEM/DEM analysis. The convergence properties of the algorithm are analysed, and illustrated on a model problem.