Related papers: Constraint-Preserving High-Order Compact OEDG Meth…

For finite element approximations of transport phenomena, it is often necessary to apply a form of limiting to ensure that the discrete solution remains well-behaved and satisfies physical constraints. However, these limiting procedures are…

We introduce discontinuous spectral-element methods of arbitrary order that are well balanced, conservative of mass, and conservative or dissipative of total energy (i.e., a mathematical entropy function) for a covariant flux formulation of…

High-order finite volume and discontinuous Galerkin methods are often stabilized by separate nonlinear devices for admissibility, entropy control, and oscillation suppression. This separation hides a simple geometric fact: all three act on…

In this work, we develop an efficient high order discontinuous Galerkin (DG) method for solving the Electrical Impedance Tomography (EIT). EIT is a highly nonlinear ill-posed inverse problem where the interior conductivity of an object is…

This paper proposes a numerical method, termed PosDiv-CDG, that provably preserves both positivity and the globally divergence-free (DF) condition at arbitrarily high order in multiple dimensions. It resolves the fundamental structural…

Recently, it was discovered that the entropy-conserving/dissipative high-order split-form discontinuous Galerkin discretizations have robustness issues when trying to solve the simple density wave propagation example for the compressible…

Compact Runge-Kutta (cRK) Discontinuous Galerkin (DG) methods, recently introduced in [Q. Chen, Z. Sun, and Y. Xing, SIAM J. Sci. Comput. SIAM J. Sci. Comput., 46: A1327-A1351, 2024], are a variant of RKDG methods for solving hyperbolic…

In earlier work [H. Liu and Z. Wang, J. Comput. Phys., 328(2017)], an arbitrary high-order conservative and energy-dissipative direct discontinuous Galerkin (DDG) scheme was developed. Although this scheme enforced solution positivity using…

Recently, two independent research efforts have been made to study the stochastic Galerkin formulation of the shallow water equations. %In particular, Bender and \"Offner developed entropy-conservative discontinuous Galerkin (DG) methods to…

The macro-element variant of the hybridized discontinuous Galerkin (HDG) method combines advantages of continuous and discontinuous finite element discretization. In this paper, we investigate the performance of the macro-element HDG method…

This work proposes a statistically enhanced framework to address the instability and limited predictive capability of conventional Galerkin-Proper Orthogonal Decomposition (Galerkin-POD) models. The method reformulates the correction of the…

In this paper, we develop a new mass conservative numerical scheme for the simulations of a class of fluid-structure interaction problems. We will use the immersed boundary method to model the fluid-structure interaction, while the fluid…

This paper establishes the minimum entropy principle (MEP) for the relativistic Euler equations with a broad class of equations of state (EOSs) and addresses the challenge of preserving the local version of the discovered MEP in high-order…

We propose two new alternative numerical schemes to solve the coupled Einstein-Euler equations in the Generalized Harmonic formulation. The first one is a finite difference (FD) Central Weighted Essentially Non-Oscillatory (CWENO) scheme on…

We study in this paper three variants of the high-order Discontinuous Galerkin (DG) method with Runge-Kutta (RK) time integration for the induction equation, analysing their ability to preserve the divergence free constraint of the magnetic…

In this paper, we present a novel class of high-order Runge--Kutta (RK) discontinuous Galerkin (DG) schemes for hyperbolic conservation laws. The new method extends beyond the traditional method of lines framework and utilizes…

A moving discontinuous Galerkin finite element method with interface conservation enforcement (MDG+ICE) is developed for solving the compressible Euler equations. The MDG+ICE method is based on the space-time DG formulation, where both flow…

We propose a high-order hybridizable discontinuous Galerkin (HDG) formulation for the fully dynamic, linear thermo-poroelasticity problem. The governing equations are formulated as a first-order hyperbolic system incorporating solid and…

Discontinuous Galerkin (DG) methods are widely adopted to discretize the radiation transport equation (RTE) with diffusive scalings. One of the most important advantages of the DG methods for RTE is their asymptotic preserving (AP)…

In this work, we design and analyze an asymptotic preserving (AP), semi-implicit finite volume scheme for the scaled compressible isentropic Euler system with a singular pressure law known as the congestion pressure law. The congestion…