Higher-order conformal decomposition FEM (CDFEM)

- The proposed CDFEM is a hybrid between classical p-FEM and fictitious domain methods.
- The CDFEM is useful for embedded domains and interface problems.
- Adaptive, automatic, higher-order mesh generation of 2D and 3D domains defined by level-set data.
- Manipulation of background mesh ensures regularity of the generated, conforming elements.
- Optimal convergence rates are achieved.

A higher-order accurate finite element method is proposed which uses automatically generated meshes based on implicit level-set data for the description of boundaries and interfaces in two and three dimensions. The method is an alternative for fictitious domain and extended finite element methods. The domain of interest is immersed in a background mesh composed by higher-order elements. The zero-level sets are identified and meshed followed by a decomposition of the cut background elements into conforming sub-elements. Adaptivity is a crucial ingredient of the method to guarantee the success of the mesh generation. It ensures the successful decomposition of cut elements and enables improved geometry descriptions and approximations. It is confirmed that higher-order accurate results with optimal convergence rates are achieved with the proposed conformal decomposition finite element method (CDFEM).