# Mathematical problems of computational decisions in the finite element method

## Abstract

Present programs for finite element analysis require the user to make numerous, critical, a-priori decisions. They often represent difficult mathematical problems and may influence strongly the accuracy and reliability of the results, the cost of the computation, and other related factors. This paper discusses some of these decisions and their mathematical aspects in the case of several typical examples. More specifically, the questions addressed here concern the effect of different mathematical formulations of the basic problem upon the results, the influence of the desired accuracy on the efficiency of the process, the selection and comparison of different types of elements, and, for nonlinear problems, the choice of efficient methods for solving the resulting finite dimensional equations. In all cases a consistent use of self-adaptive techniques is strongly indicated.

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