Stagnation in the p-version of the finite element methodстатья
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Аннотация:A special feature of the p-version of the finite element method for solving a differential boundary value problem stated in the form of minimizing a quadratic functional on a certain set is studied. This special feature (stagnation) results in approximate solutions remaining unchanged on finite numbers of increasing finite dimensional subsets of increasing dimension, in which solutions are sought. Necessary and sufficient conditions for the existence of this feature are found, and the stagnation effect is interpreted for a specially constructed example. For the adaptive p-version of the finite element approach, a modified strategy is proposed that takes this feature into account and thus improves the reliability of the method.