An Immersed Weak Galerkin Method For Elliptic Interface Problems
For computational scientists solving interface problems, this method simplifies mesh generation by allowing Cartesian grids, though it is an incremental extension of existing weak Galerkin and immersed methods.
The paper develops an immersed weak Galerkin method for elliptic interface problems that works on non-interface-aligned meshes, enabling uniform Cartesian grids. Error estimates in energy norm are proven and numerical results validate the method.
In this paper, we present an immersed weak Galerkin method for solving second-order elliptic interface problems. The proposed method does not require the meshes to be aligned with the interface. Consequently, uniform Cartesian meshes can be used for nontrivial interfacial geometry. We show the existence and uniqueness of the numerical algorithm, and prove the error estimates for the energy norm. Numerical results are reported to demonstrate the performance of the method.