Mathematics - Numerical Analysis

Construction of Basis Functions for the Geometry Conforming Immersed Finite Element Method

This paper develops a high-order selective discontinuous Galerkin (SDG) method for solving elliptic interface problems on interface-unfitted Cartesian meshes. This method applies the discontinuous Galerkin (DG) formulation on interface elements and the continuous Galerkin (CG) formulation elsewhere.

Slimane Adjerid, Tao Lin, Haroun Meghaichi

Oct 13, 2025