相关论文: A subspace correction method for discontinuous Gal…

In this paper we design and analyze a uniform preconditioner for a class of high order Discontinuous Galerkin schemes. The preconditioner is based on a space splitting involving the high order conforming subspace and results from the…

We introduce a family of discontinuous Galerkin methods to approximate the eigenvalues and eigenfunctions of a Stokes-Brinkman type of problem based in the interior penalty strategy. Under the standard assumptions on the meshes and a…

The aim of this paper is to establish a theory of Galerkin approximations to the space of convex and compact subsets of $\R^d$ with favorable properties, both from a theoretical and from a computational perspective. These Galerkin spaces…

Recently, it was discovered that the entropy-conserving/dissipative high-order split-form discontinuous Galerkin discretizations have robustness issues when trying to solve the simple density wave propagation example for the compressible…

We develop a high order accurate numerical method for solving the elastic wave equation in second-order form. We hybridize the computationally efficient Cartesian grid formulation of finite differences with geometrically flexible…

In two and three dimension we analyze discontinuous Galerkin methods for the acoustic problem. The acoustic fluid that we consider on this paper is inviscid, leading to a linear eigenvalue problem. The acoustic problem is written, in first…

We consider a space-time finite element method on fully unstructured simplicial meshes for optimal sparse control of semilinear parabolic equations. The objective is a combination of a standard quadratic tracking-type functional including a…

Based on a discontinuous Galerkin method in the spatial directions and an improved implicit-explicit pressure-correction scheme in the temporal direction, this paper discusses a fully discrete scheme for the…

The goal of this work is to present a fast and viable approach for the numerical solution of the high-contrast state problems arising in topology optimization. The optimization process is iterative, and the gradients are obtained by an…

Subcell limiting strategies for discontinuous Galerkin spectral element methods do not provably satisfy a semi-discrete cell entropy inequality. In this work, we introduce an extension to the subcell and monolithic convex limiting…

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 present an a priori error analysis for solving the unsteady advection equation on cut cell meshes along a straight ramp in two dimensions. The space discretization uses a lowest order upwind-type discontinuous Galerkin…

In this paper, we investigate the combination of a linear continuous interior penalty type and a non-linear artificial diffusion stabilisation applied to the transport problem, based on continuous Galerkin finite elements in space. This…

We derive well-posed boundary conditions for the linearized Serre equations in one spatial dimension by utilizing the energy method. An energy stable and conservative discontinuous Galerkin spectral element method with simple upwind…

We propose and investigate new robust preconditioners for space-time Isogeometric Analysis of parabolic evolution problems. These preconditioners are based on a time parallel multigrid method. We consider a decomposition of the space-time…

In this paper, we develop an arbitrary-order locking-free enriched Galerkin method for the linear elasticity problem using the stress-displacement formulation in both two and three dimensions. The method is based on the mixed discontinuous…

We consider a model convection-diffusion problem and present our recent numerical and analysis results regarding mixed finite element formulation and discretization in the singular perturbed case when the convection term dominates the…

In this work, we apply a time-space adaptive discontinuous Galerkin method using the elliptic reconstruction technique with a robust (in P\'eclet number) elliptic error estimator in space, for the convection dominated parabolic problems…

This article investigates matrix-free higher-order discontinuous Galerkin discretizations of the Navier--Stokes equations for incompressible flows with variable viscosity. The viscosity field may be prescribed analytically or governed by a…

This work is concerned with the derivation of a robust a posteriori error estimator for a discontinuous Galerkin method discretisation of linear non-stationary convection-diffusion initial/boundary value problems and with the implementation…