4 papers
Hyperbolicity-Preserving Stochastic Galerkin Methods for Conservation Laws Based on Associative Truncated Products on Polynomial Spaces
Haroun Meghaichi, Yulong Xing
Stochastic Galerkin discretizations of nonlinear hyperbolic conservation laws may lose hyperbolicity because the standard pseudospectral product is generally nonassociative, leadin…
A Priori Error Analysis of a High-Order Selective Discontinuous Galerkin Method for Elliptic Interface Problems
Fang Liu, Haroun Meghaichi, Xu Zhang
This paper develops a high-order selective discontinuous Galerkin (SDG) method for solving elliptic interface problems on interface-unfitted Cartesian meshes. This method applies t…
Construction of Basis Functions for the Geometry Conforming Immersed Finite Element Method
Slimane Adjerid, Tao Lin, Haroun Meghaichi
The Frenet apparatus is a new framework for constructing high order geometry-conforming immersed finite element functions for interface problems. In this report, we present a proce…
The Frenet immersed finite element method for elliptic interface problems: An error analysis
Slimane Adjerid, Tao Lin, Haroun Meghaichi
This article presents an error analysis of the recently introduced Frenet immersed finite element (IFE) method. The Frenet IFE space employed in this method is constructed to be lo…