Related papers: A posteriori error estimates for discontinuous Gal…
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…
We present a priori and a posteriori error analysis of a high order hybridizable discontinuous Galerkin (HDG) method applied to a semi-linear elliptic problem posed on a piecewise curved, non polygonal domain. We approximate $\Omega$ by a…
The purpose of the research is to find the numerical solutions to the system of time dependent nonlinear parabolic partial differential equations (PDEs) utilizing the Modified Galerkin Weighted Residual Method (MGWRM) with the help of…
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.…
We propose an algorithm to numerically determined whether a second-order linear PDE problem satisfying a Garding inequality is well-posed. This algorithm further provides a lower bound to the inf-sup constant of the weak formulation, which…
In this paper, discontinuous Galerkin finite element methods are applied to one dimensional Rosenau equation. Theoretical results including consistency, a priori bounds and optimal error estimates are established for both semidiscrete and…
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…
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 present an a posteriori error analysis for one-dimensional random hyperbolic systems of conservation laws. For the discretization of the random space we consider the Non-Intrusive Spectral Projection method, the spatio-temporal…
This paper presents a fully discrete numerical scheme for one-dimensional nonlocal wave equations and provides a rigorous theoretical analysis. To facilitate the spatial discretization, we introduce an auxiliary variable analogous to the…
The weak Galerkin (WG) finite element method has shown great potential in solving various type of partial differential equations. In this paper, we propose an arbitrary order locking-free WG method for solving linear elasticity problems,…
A conforming discontinuous Galerkin (DG) finite element method has been introduced in [21] on simplicial meshes, which has the flexibility of using discontinuous approximation and the simplicity in formulation of the classic continuous…
An abstract property (H) is the key to a complete a priori error analysis in the (discrete) energy norm for several nonstandard finite element methods in the recent work [Lowest-order equivalent nonstandard finite element methods for…
We extend the applicability of the popular interior-penalty discontinuous Galerkin (dG) method discretizing advection-diffusion-reaction problems to meshes comprising extremely general, essentially arbitrarily-shaped element shapes. In…
Discontinuous Galerkin (DG) methods for hyperbolic partial differential equations (PDEs) with explicit time-stepping schemes, such as strong stability-preserving Runge-Kutta (SSP-RK), suffer from time-step restrictions that are…
The numerical simulation of complex physical processes requires the use of economical discrete models. This lecture presents a general paradigm of deriving a posteriori error estimates for the Galerkin finite element approximation of…
In the present work, we examine and analyze an hp-version interior penalty discontinuous Galerkin finite element method for the numerical approximation of a steady fluid system on computational meshes consisting of polytopic elements on the…
A new interior-exterior penalty method for solving quasi-variational inequality and pseudo-monotone operators arising in two-dimensional point contact problem has been analyzed and developed in discontinuous Galerkin finite volume method…
We consider the discretization of the $p$-Laplacian equation with an interior penalty discontinuous Galerkin method. We prove novel trace-type inverse estimates, leading to unconditional stability of the method. Further, $hp$-version a…
We present a new family of high order accurate fully discrete one-step Discontinuous Galerkin (DG) finite element schemes on moving unstructured meshes for the solution of nonlinear hyperbolic PDE in multiple space dimensions, which may…