Related papers: BDDC Algorithms for Advection-diffusion problems w…
We propose and analyze an iterative high-order hybridized discontinuous Galerkin (iHDG) discretization for linear partial differential equations. We improve our previous work (SIAM J. Sci. Comput. Vol. 39, No. 5, pp. S782--S808) in several…
The accurate numerical simulation of turbulent incompressible flows is a challenging topic in computational fluid dynamics. For discretisation methods to be robust in the under-resolved regime, mass conservation as well as energy stability…
We develop a hybrid spatial discretization for the wave equation in second order form, based on high-order accurate finite difference methods and discontinuous Galerkin methods. The hybridization combines computational efficiency of finite…
We consider the finite element solution of time-harmonic wave propagation problems in heterogeneous media with hybridizable discontinuous Galerkin (HDG) methods. In the case of homogeneous media, it has been observed that the iterative…
A new hybridizable discontinuous Galerkin method, named the CHDG method, is proposed for solving time-harmonic scalar wave propagation problems. This method relies on a standard discontinuous Galerkin scheme with upwind numerical fluxes and…
We investigate numerical behaviour of a convection diffusion equation with random coefficients by approximating statistical moments of the solution. Stochastic Galerkin approach, turning the original stochastic problem to a system of…
We consider the bilinear optimal control of an advection-reaction-diffusion system, where the control arises as the velocity field in the advection term. Such a problem is generally challenging from both theoretical analysis and algorithmic…
In this paper, we present an embedded staggered discontinuous Galerkin method for the convection-diffusion equation. The new method combines the advantages of staggered discontinuous Galerkin (SDG) and embedded discontinuous Galerkin (EDG)…
We propose a multilevel approach for trace systems resulting from hybridized discontinuous Galerkin (HDG) methods. The key is to blend ideas from nested dissection, domain decomposition, and high-order characteristic of HDG discretizations.…
In this paper, we introduce a new, fast data assimilation algorithm for a 2D linear advection equation with divergence-free coefficients. We first apply the nodal discontinuous Galerkin (DG) method to discretize the advection equation, and…
We study the convergence of iterative linear solvers for discontinuous Galerkin discretizations of systems of hyperbolic conservation laws with polygonal mesh elements compared with that of traditional triangular elements. We solve the…
This paper develops and analyzes a class of semi-discrete and fully discrete weak Galerkin finite element methods for unsteady incompressible convective Brinkman-Forchheimer equations. For the spatial discretization, the methods adopt the…
In this work we study arbitrary-order hybrid discretizations of Friedrichs systems. Friedrichs systems provide a framework that goes beyond the standard classification of partial differential equations into hyperbolic or elliptic, and are…
Methods for solving hyperbolic systems typically depend on unknown ordering (e.g., Gauss-Seidel, or sweep/wavefront/marching methods) to achieve good convergence. For many discretisations, mesh types or decompositions these methods do not…
A direct discontinuous Galerkin (DDG) finite element method is developed for solving fractional convection-diffusion and Schr\"{o}dinger type equations with a fractional Laplacian operator of order $\alpha$ $(1<\alpha<2)$. The fractional…
Subsurface flows are commonly modeled by advection-diffusion equations. Insufficient measurements or uncertain material procurement may be accounted for by random coefficients. To represent, for example, transitions in heterogeneous media,…
This paper considers the optimal boundary control of chemical systems described by advection-diffusion-reaction (ADR) equations. We use a discontinuous Galerkin finite element method (DG-FEM) for the spatial discretization of the governing…
In this paper, we develop an adaptive Generalized Multiscale Discontinuous Galerkin Method (GMs-DGM) for a class of high-contrast flow problems, and derive a-priori and a-posteriori error estimates for the method. Based on the a-posteriori…
We propose an embedded discontinuous Galerkin (EDG) method to approximate the solution of a distributed control problem governed by convection diffusion PDEs, and obtain optimal a priori error estimates for the state, dual state, their…
We consider a model convection-diffusion problem and present useful connections between the finite differences and finite element discretization methods. We introduce a general upwinding Petrov-Galerkin discretization based on bubble…