Related papers: Discontinuous Galerkin finite element method for t…
We develop a family of cut finite element methods of different orders based on the discontinuous Galerkin framework, for hyperbolic conservation laws with stationary interfaces in both one and two space dimensions, and for moving interfaces…
We present a novel high-order accurate nodal discontinuous Galerkin (DG) method for solving nonlinear hyperbolic systems of partial differential equations (PDEs) on fully unstructured three-dimensional polyhedral meshes. A mesh generator is…
Electron devices based on graphene have lately received a considerable interest; in fact, they could represent the ultimate miniaturization, since the active area is only one atom tick. However, the gapless dispersion relation of graphene…
In this paper, we discuss the application of the Generalized Finite Element Method (GFEM) to approximate the solutions of quasilinear elliptic equations with multiple interfaces in one dimensional space. The problem is characterized by…
In this article, interior penalty discontinuous Galerkin methods using immersed finite element functions are employed to solve parabolic interface problems. Typical semi-discrete and fully discrete schemes are presented and analyzed.…
In this work, we propose an accurate, robust, and stable discretization of the gamma-based compressible multicomponent model by Shyue [J. Comput. Phys., 142 (1998), 208-242] where each component follows a stiffened gas equation of state…
We present a realizability-preserving numerical method for solving a spectral two-moment model to simulate the transport of massless, neutral particles interacting with a steady background material moving with relativistic velocities. The…
A semidiscrete Galerkin finite element method applied to time-fractional diffusion equations with time-space dependent diffusivity on bounded convex spatial domains will be studied. The main focus is on achieving optimal error results with…
In this paper we present a new multiscale discontinuous Petrov--Galerkin method (MsDPGM) for multiscale elliptic problems. This method utilizes the classical oversampling multiscale basis in the framework of Petrov--Galerkin version of…
There has been an arising trend of adopting deep learning methods to study partial differential equations (PDEs). This article is to propose a Deep Learning Galerkin Method (DGM) for the closed-loop geothermal system, which is a new coupled…
In this paper, we describe a stable finite element formulation for advection-diffusion-reaction problems that allows for robust automatic adaptive strategies to be easily implemented. We consider locally vanishing, heterogeneous, and…
This paper generalizes the earlier work on the energy-based discontinuous Galerkin method for second-order wave equations to fourth-order semilinear wave equations. We first rewrite the problem into a system with a second-order spatial…
This research article discusses a numerical solution of the radiative transfer equation based on the weak Galerkin finite element method. We discretize the angular variable by means of the discrete-ordinate method. Then the resulting…
We propose and analyze a time-stepping discontinuous Petrov-Galerkin method combined with the continuous conforming finite element method in space for the numerical solution of time-fractional subdiffusion problems. We prove the existence,…
This work is concerned with the analysis of a space-time finite element discontinuous Galerkin method on polytopal meshes (XT-PolydG) for the numerical discretization of wave propagation in coupled poroelastic-elastic media. The…
A new finite element method with discontinuous approximation is introduced for solving second order elliptic problem. Since this method combines the features of both conforming finite element method and discontinuous Galerkin (DG) method,…
We present a collection of MATLAB routines using discontinuous Galerkin finite elements method (DGFEM) for solving steady-state diffusion-convection-reaction equations. The code employs the sparse matrix facilities of MATLAB with…
We develop a novel and efficient discontinuous Galerkin spectral element method (DG-SEM) for the spherical rotating shallow water equations in vector invariant form. We prove that the DG-SEM is energy stable, and discretely conserves mass,…
Numerically solving high-dimensional random parametric PDEs poses a challenging computational problem. It is well-known that numerical methods can greatly benefit from adaptive refinement algorithms, in particular when functional…
A discontinuous Galerkin time-domain (DGTD) method based on dynamically adaptive Cartesian meshes (ACM) is developed for a full-wave analysis of electromagnetic fields in dispersive media. Hierarchical Cartesian grids offer simplicity close…