p- and h-type adaptive mesh generation

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Abstract
Adaptive mesh generation involves the improvement of finite elements on the basis of error estimates by either refining the mesh (h‐type refinement) or improving the trial function (p‐type refinement). In this paper, both methods are employed in conjunction, thereby reaping the advantages of both approaches. The strategy is tested with two different error criteria, one based on nodal perturbations and the other on discontinuities of the magnetic field or the flux density between neighboring elements. Forces on permanent magnets are computed to demonstrate the method.