相关论文: Space-time hp finite elements for heat evolution i…

This paper proposes an efficient ADER (Arbitrary DERivatives in space and time) discontinuous Galerkin (DG) scheme to directly solve the Hamilton-Jacobi equation. Unlike multi-stage Runge-Kutta methods used in the Runge-Kutta DG (RKDG)…

The two-fluid plasma model has a wide range of timescales which must all be numerically resolved regardless of the timescale on which plasma dynamics occurs. The answer to solving numerically stiff systems is generally to utilize…

In this paper we study the numerical method for approximating the random periodic solution of semiliear stochastic evolution equations. The main challenge lies in proving a convergence over an infinite time horizon while simulating…

We present a space-time finite element method for the heat equation that computes quasi-optimal approximations with respect to natural norms while incorporating local mesh refinements in space-time. The discretized problem is solved with a…

We propose a fourth-order unfitted characteristic finite element method to solve the advection-diffusion equation on time-varying domains. Based on a characteristic-Galerkin formulation, our method combines the cubic MARS method for…

In this work we investigate the advantages of multiscale methods in Petrov-Galerkin (PG) formulation in a general framework. The framework is based on a localized orthogonal decomposition of a high dimensional solution space into a low…

Critical points of energy functionals, which are of broad interest, for instance, in physics and chemistry, in solid and quantum mechanics, in material science, or in general diffusion-reaction models arise as solutions to the associated…

In this paper, we present an interior penalty discontinuous Galerkin finite element scheme for solving diffusion problems with strong anisotropy arising in magnetized plasmas for fusion applications. We demonstrate the accuracy produced by…

We introduce a family of Galerkin finite element methods which are constructed via recovery operators over element-wise discontinuous approximation spaces. This new family, termed collectively as recovered finite element methods (R-FEM) has…

The incompressible Euler equations are an important model system in computational fluid dynamics. Fast high-order methods for the solution of this time-dependent system of partial differential equations are of particular interest: due to…

We present a space-time continuous-Galerkin finite element method for solving incompressible Navier-Stokes equations. To ensure stability of the discrete variational problem, we apply ideas from the variational multi-scale method. The…

We present and analyze a new embedded--hybridized discontinuous Galerkin finite element method for the Stokes problem. The method has the attractive properties of full hybridized methods, namely an $H({\rm div})$-conforming velocity field,…

In this paper, we introduce and analyze a space-time $p$-adaptive discontinuous Galerkin method for nonlinear acoustics. We first present the underlying mathematical model, which is based on a recently derived formulation involving, in…

This contribution focuses on the development of Model Order Reduction (MOR) for one-way coupled steady state linear thermomechanical problems in a finite element setting. We apply Proper Orthogonal Decomposition (POD) for the computation of…

This paper proposes and analyzes two fully discrete mixed interior penalty discontinuous Galerkin (DG) methods for the fourth order nonlinear Cahn-Hilliard equation. Both methods use the backward Euler method for time discretization and…

This study presents a fair performance comparison of the continuous finite element method, the symmetric interior penalty discontinuous Galerkin method, and the hybridized discontinuous Galerkin method. Modern implementations of high-order…

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…

In (J. Comput. Phys., 417, 109577, 2020) we introduced a space-time embedded-hybridizable discontinuous Galerkin method for the solution of the incompressible Navier-Stokes equations on time-dependent domains of which the motion of the…

In additive manufacturing, the fabrication sequence has a large influence on the quality of manufactured components. While planning of the fabrication sequence is typically performed after the component has been designed, recent…

We design and analyze a new adaptive stabilized finite element method. We construct a discrete approximation of the solution in a continuous trial space by minimizing the residual measured in a dual norm of a discontinuous test space that…