Related papers: A Discontinuous Galerkin Finite Element Model for …
Stochastic Galerkin methods can quantify uncertainty at a fraction of the computational expense of conventional Monte Carlo techniques, but such methods have rarely been studied for modelling shallow water flows. Existing stochastic shallow…
This paper explores static non-uniform grid solvers that adapt three raster-based flood models on an optimised non-uniform grid: the second-order discontinuous Galerkin (DG2) model representing the modelled data as piecewise-planar fields,…
Offline computation is an essential component in most multiscale model reduction techniques. However, there are multiscale problems in which offline procedure is insufficient to give accurate representations of solutions, due to the fact…
Wave propagation in real media is affected by various non-trivial physical phenomena, e.g., anisotropy, an-elasticity and dissipation. Assumptions on the stress-strain relationship are an integral part of seismic modeling and determine the…
We study the use of the hybridizable discontinuous Galerkin (HDG) method for numerically solving fractional diffusion equations of order $-\alpha$ with $-1<\alpha<0$. For exact time-marching, we derive optimal algebraic error estimates…
As an extension of our previous work in Sun et.al (2018) [41], we develop a discontinuous Galerkin method for solving cross-diffusion systems with a formal gradient flow structure. These systems are associated with non-increasing entropy…
We design an arbitrary high-order accurate nodal discontinuous Galerkin spectral element approximation for the nonlinear two dimensional shallow water equations with non-constant, possibly discontinuous, bathymetry on unstructured, possibly…
In this paper, we consider a class of discontinuous Galerkin (DG) methods for one-dimensional nonlocal diffusion (ND) problems. The nonlocal models, which are integral equations, are widely used in describing many physical phenomena with…
Wave propagation problems for heterogeneous media are known to have many applications in physics and engineering. Recently, there has been an increasing interest in stochastic effects due to the uncertainty, which may arise from impurities…
Discontinuous Galerkin (DG) discretizations with exact representation of the geometry and local polynomial degree adaptivity are revisited. Hybridization techniques are employed to reduce the computational cost of DG approximations and…
Motivated by applications to numerical simulation of flows in highly heterogeneous porous media, we develop multiscale finite element methods for second order elliptic equations. We discuss a multiscale model reduction technique in the…
We develop a locally conservative, finite element method for simulation of two-phase flow on quadrilateral meshes that minimize the number of degrees of freedom (DoFs) subject to accuracy requirements and the DoF continuity constraints. We…
In this paper, we propose a unified and high order accurate fully-discrete one-step ADER Discontinuous Galerkin method for the simulation of linear seismic waves in the sea bottom that are generated by the propagation of free surface water…
The mixed form of the Cahn-Hilliard equations is discretized by the hybridizable discontinuous Galerkin method. For any chemical energy density, existence and uniqueness of the numerical solution is obtained. The scheme is proved to be…
We present an embedded-hybridizable discontinuous Galerkin finite element method for the total pressure formulation of the quasi-static poroelasticity model. Although the displacement and the Darcy velocity are approximated by discontinuous…
We introduce a new mixed discontinuous/continuous Galerkin finite element for solving the 2- and 3-dimensional wave equations and equations of incompressible flow. The element, which we refer to as P1dg-P2, uses discontinuous piecewise…
We develop a high-order hybridized discontinuous Galerkin (HDG) method for a linear degenerate elliptic equation arising from a two-phase mixture of mantle convection or glacier dynamics. We show that the proposed HDG method is well-posed…
Robust and accurate schemes are designed to simulate the coupling between subsurface and overland flows. The coupling conditions at the interface enforce the continuity of both the normal flux and the pressure. Richards' equation governing…
We present a novel approach to the simulation of miscible displacement by employing adaptive enriched Galerkin finite element methods (EG) coupled with entropy residual stabilization for transport. In particular, numerical simulations of…
In this work a non-conservative balance law formulation is considered that encompasses the rotating, compressible Euler equations for dry atmospheric flows. We develop a semi-discretely entropy stable discontinuous Galerkin method on…