Abstract
Finite elements that are the shape of an arbitrary polygon offer several advantages over traditional triangles and quadrilaterals. Elements with linear and quadratic precision have been reported, but they have interpolatory bases. Hierarchical bases are described here. Elements with up to cubic precision are tested and it is confirmed that they give the expected convergence as the mesh density is increased, even when the elements are reentrant polygons. A magnetostatic problem is solved with elements of different orders.
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