P-FEM

p-FEM or the p-version of the finite element method is a numerical method for solving partial differential equations. It is a discretization strategy in which the finite element mesh is fixed and the polynomial degrees of elements are increased such that the lowest polynomial degree, denoted by ${\displaystyle p_{\min }}$, approaches infinity. This is in contrast with the "h-version" or "h-FEM", a widely used discretization strategy, in which the polynomial degrees of elements are fixed and the mesh is refined such that the diameter of the largest element, denoted by ${\displaystyle h_{\max }}$ approaches zero.

It was demonstrated on the basis of a linear elastic fracture mechanics problem that sequences of finite element solutions based on the p-version converge faster than sequences based on the h-version by Szabó and Mehta in 1978. The theoretical foundations of the p-version were established in a paper published Babuška, Szabó and Katz in 1981 where it was shown that for a large class of problems the asymptotic rate of convergence of the p-version in energy norm is at least twice that of the h-version, assuming that quasi-uniform meshes are used. Additional computational results and evidence of faster convergence of the p-version were presented by Babuška and Szabó in 1982.

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