A higher-order accurate conformal decomposition finite element method (CDFEM) is proposed, using an explicit boundary description of the domain. A level-set concept is introduced which converts the explicit B-rep geometry based on NURBSs to an implicit representation. This concept also applies to higher-order fictitious domain methods (FDMs) which are often based on implicit descriptions. In the proposed CDFEM, an arbitrary, non-conforming background mesh is introduced and manipulated to capture non-smooth features of the boundary such as corners and to ensure shape-regular elements. Elements that are cut by the boundary are decomposed into conforming sub-elements. The final mesh composed by higher-order Lagrange elements enables higher-order accurate approximations in the context of the FEM. Special emphasis is on the fact that NURBSs feature reduced continuity between knot spans which must be properly considered in the mesh generation, not only at corners.
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