Manuscript

Hyperbolicity-Preserving Stochastic Galerkin Methods for Conservation Laws Based on Associative Truncated Products on Polynomial Spaces
Stochastic Galerkin discretizations of nonlinear hyperbolic conservation laws may lose hyperbolicity because the standard pseudospectral product is generally nonassociative, leading to non-commuting blocks in the flux Jacobian matrix. We develop a novel framework for constructing hyperbolicity-preserving stochastic Galerkin systems based on associative truncated products on polynomial spaces.
Haroun Meghaichi, Yulong Xing
Jun 1, 2026
Cite DOI arXiv
A Priori Error Analysis of a High-Order Selective Discontinuous Galerkin Method for Elliptic Interface Problems
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.
Fang Liu, Haroun Meghaichi, Xu Zhang
May 21, 2026
Cite arXiv
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
Cite arXiv