Related papers: Discontinuous Galerkin methods for the Laplace-Bel…
In this paper we present the discontinuous Galerkin method to solve the problem of the two-dimensional air pollution model. The resulting system of ordinary differential equations is called the semidiscrete formulation. We show the…
This paper focuses on the adaptive discontinuous Galerkin (DG) methods for the tempered fractional (convection) diffusion equations. The DG schemes with interior penalty for the diffusion term and numerical flux for the convection term are…
In this paper, we develop a Discontinuous Galerkin (DG) method for solving H(curl)-elliptic hemivariational inequalities. By selecting an appropriate numerical flux, we construct an Interior Penalty Discontinuous Galerkin (IPDG) scheme. A…
This paper is concerned with developing accurate and efficient numerical methods for fully nonlinear second order elliptic and parabolic partial differential equations (PDEs) in multiple spatial dimensions. It presents a general framework…
This work presents uniform preconditioners for the discrete Laplace--Beltrami operator on hypersurfaces. In particular, within the framework of fast auxiliary space preconditioning (FASP), we develop efficient and user-friendly multilevel…
This paper is concerned with using discontinuous Galerkin isogeometric analysis (dGIGA) as a numerical treatment of Diffusion problems on orientable surfaces $\Omega \subset \mathbb{R}^3$. The computational domain or surface considered…
We present and analyze a discontinuous Galerkin method for the numerical modelling of the non-linear fully-coupled thermo-poroelastic problem. For the spatial discretization, we design a high-order discontinuous Galerkin method on polygonal…
We propose and analyse a fully-discrete discontinuous Galerkin time-stepping method for parabolic Hamilton--Jacobi--Bellman equations with Cordes coefficients. The method is consistent and unconditionally stable on rather general…
We present a posteriori error analysis in the supremum norm for the symmetric interior penalty discontinuous Galerkin method for the elliptic obstacle problem. We construct discrete barrier functions based on appropriate corrections of the…
We derive and analyze a symmetric interior penalty discontinuous Galerkin scheme for the approximation of the second-order form of the radiative transfer equation in slab geometry. Using appropriate trace lemmas, the analysis can be carried…
Discontinuous Galerkin (DG) methods for the numerical solution of partial differential equations have enjoyed considerable success because they are both flexible and robust: They allow arbitrary unstructured geometries and easy control of…
This paper provides the semi-discrete scheme by the central local discontinuous Galerkin method for space fractional diffusion equation on two sets of overlapping cells, and then we give the stability analysis and error estimates for the…
In this paper, a second-order linearized discontinuous Galerkin method on general meshes, which treats the backward differentiation formula of order two (BDF2) and Crank-Nicolson schemes as special cases, is proposed for solving the…
The goal of this paper is to create a fruitful bridge between the numerical methods for approximating partial differential equations (PDEs) in fluid dynamics and the (iterative) numerical methods for dealing with the resulting large linear…
We propose and analyze discontinuous Galerkin (dG) approximations to 3D-1D coupled systems which model diffusion in a 3D domain containing a small inclusion reduced to its 1D centerline. Convergence to weak solutions of a steady state…
Linear wave equations sourced by a Dirac delta distribution $\delta(x)$ and its derivative(s) can serve as a model for many different phenomena. We describe a discontinuous Galerkin (DG) method to numerically solve such equations with…
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…
The discontinuous Galerkin dG method provides a robust and flexible technique for the time integration of fractional diffusion problems. However, a practical implementation uses coefficients defined by integrals that are not easily…
This chapter reviews and compares discontinuous Galerkin time-stepping methods for the numerical approximation of second-order ordinary differential equations, particularly those stemming from space finite element discretization of wave…
We extend the discontinuous Galerkin (DG) framework to the analysis of first-order hyperbolic and advection-dominated problems posed on implicitly defined surfaces. The focus will be on the hyperbolic part, which is discretised using a…