Higher‐order conformal decomposition finite element method

Abstract

Numerical simulations of structures using higher-order finite elements is still a challenging task, in particular for domains with curved boundaries. A new higher-order accurate approach is proposed, combining the advantages of the classical p-FEM with embedded domain methods. Boundaries and/or interfaces are described implicitly using the level set method. In the elements cut by the zero level set, an automatic decomposition into interface aligned, i.e. conforming sub-elements is realized. Transfinite mappings are utilized to construct higher-order sub-elements by mappings of reference elements to the two sides of the boundary or interface. It is shown that although the resulting sub-elements are not always well-shaped, optimal convergence rates are possible.