skärelement

Skärelement is a term used in finite element analysis and mesh-based simulations to describe a mesh element that is intersected by an interface within the computational domain. An element is considered a skärelement when a geometric boundary, such as a material or phase boundary, passes through its interior, causing part of the element to belong to one region while the remainder belongs to another. This situation arises in unfitted or immersed mesh approaches, where the mesh is not aligned to all interfaces, and in problems involving multiphase flow, multi-material solids, or fracture.

In practice, the interface is represented by a separate description, such as a level-set function or a geometric surface. The portion of the skärelement lying in each region contributes to the overall solution according to the material properties of that region. Numerical integration is performed over the subregions defined by the cut, and the element contributes to the global system through these split quadrature regions. Advanced methods, such as extended finite element methods (XFEM) and cut finite element methods (cutFEM), explicitly address the presence of skärelements by enriching the approximation space or applying specialized stabilization techniques.

Key challenges associated with skärelements include ill-conditioning when the cut fraction is very small, accurate integration on irregular subdomains, and consistent enforcement of boundary and interface conditions. Solutions often involve stabilization terms (for example, ghost penalties), adaptive refinement near interfaces, and carefully designed quadrature rules to maintain accuracy and stability.

Applications span two-phase and multi-material problems in fluid and solid mechanics, porous media flows, and fracture or interface-dominated simulations. Understanding skärelements is essential for reliable simulations in scenarios where interfaces cut through a regular mesh.