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We present a high-order implicit large-eddy simulation (ILES) approach for simulating transitional turbulent flows. The approach consists of an Interior Embedded Discontinuous Galerkin (IEDG) method for the discretization of the…

Fluid Dynamics · Physics 2016-05-04 Pablo Fernandez , Ngoc-Cuong Nguyen , Xevi Roca , Jaime Peraire

The unified gas kinetic scheme (UGKS) of K. Xu et al. [K. Xu and J.-C. Huang, J. Comput. Phys., 229, pp. 7747--7764, 2010], originally developed for multiscale gas dynamics problems, is applied in this paper to a linear kinetic model of…

Numerical Analysis · Mathematics 2014-01-24 Luc Mieussens

High order implicit-explicit (IMEX) methods are often desired when evolving the solution of an ordinary differential equation that has a stiff part that is linear and a non-stiff part that is nonlinear. This situation often arises in…

Numerical Analysis · Mathematics 2020-07-16 Adi Ditkowski , Sigal Gottlieb , Zachary J. Grant

The concern of the present work is the introduction of a very efficient Asymptotic Preserving scheme for the resolution of highly anisotropic diffusion equations. The characteristic features of this scheme are the uniform convergence with…

Numerical Analysis · Mathematics 2014-04-08 Pierre Degond , Alexei Lozinski , Jacek Narski , Claudia Negulescu

In this paper we propose and analyze finite element discontinuous Galerkin methods for the one- and two-dimensional stochastic Maxwell equations with multiplicative noise. The discrete energy law of the semi-discrete DG methods were…

Numerical Analysis · Mathematics 2022-04-21 Jiawei Sun , Chi-Wang Shu , Yulong Xing

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…

Numerical Analysis · Mathematics 2021-09-01 Roberto J. Cier , Sergio Rojas , Victor M. Calo

In numerical time-integration with implicit-explicit (IMEX) methods, a within-step adaptable decomposition called residual balanced decomposition is introduced. With this decomposition, the requirement of a small enough residual in the…

Numerical Analysis · Mathematics 2019-02-11 Savio B. Rodrigues

In this paper, we present and analyze an interior penalty discontinuous Galerkin method for the distributed elliptic optimal control problems. It is based on a reconstructed discontinuous approximation which admits arbitrarily high-order…

Numerical Analysis · Mathematics 2026-01-05 Ruo Li , Haoyang Liu , Jun Yin

In this work, we propose and investigate stable high-order collocation-type discretisations of the discontinuous Galerkin method on equidistant and scattered collocation points. We do so by incorporating the concept of discrete least…

Numerical Analysis · Mathematics 2021-02-24 Jan Glaubitz , Philipp Oeffner

The study of uncertainty propagation poses a great challenge to design numerical solvers with high fidelity. Based on the stochastic Galerkin formulation, this paper addresses the idea and implementation of the first flux reconstruction…

Computational Physics · Physics 2021-12-14 Tianbai Xiao , Jonas Kusch , Julian Koellermeier , Martin Frank

We present a novel discontinuous Galerkin finite element method for numerical simulations of the rotating thermal shallow water equations in complex geometries using curvilinear meshes, with arbitrary accuracy. We derive an entropy…

Numerical Analysis · Mathematics 2024-01-19 Kieran Ricardo , Kenneth Duru , David Lee

In this paper we consider the semi-discretization in space of a first order scalar transport equation. For the space discretization we use standard continuous finite elements. To obtain stability we add a penalty on the jump of the gradient…

Numerical Analysis · Mathematics 2021-09-17 Erik Burman

The prediction of thermo-mechanical behaviour of heterogeneous materials such as heat and moisture transport is strongly influenced by the uncertainty in parameters. Such materials occur e.g. in historic buildings, and the durability…

Computational Engineering, Finance, and Science · Computer Science 2013-03-19 A. Kucerova , J. Sykora , B. Rosic , H. G. Matthies

We present analysis of two lowest-order hybridizable discontinuous Galerkin methods for the Stokes problem, while making only minimal regularity assumptions on the exact solution. The methods under consideration have previously been shown…

Numerical Analysis · Mathematics 2023-07-07 Aaron Baier-Reinio , Sander Rhebergen , Garth N. Wells

This paper develops and analyzes an interior penalty discontinuous Galerkin (IPDG) method using piecewise linear polynomials for the indefinite time harmonic Maxwell equations with the impedance boundary condition in the three dimensional…

Numerical Analysis · Mathematics 2012-12-11 Xiaobing Feng , Haijun Wu

We consider the discretization of electromagnetic wave propagation problems by a discontinuous Galerkin Method based on Trefftz polynomials. This method fits into an abstract framework for space-time discontinuous Galerkin methods for which…

Numerical Analysis · Mathematics 2014-12-10 Herbert Egger , Fritz Kretzschmar , Sascha M. Schnepp , Thomas Weiland

Implicit-explicit (IMEX) time stepping methods can efficiently solve differential equa- tions with both stiff and nonstiff components. IMEX Runge-Kutta methods and IMEX linear multistep methods have been studied in the literature. In this…

Numerical Analysis · Mathematics 2013-03-26 Hong Zhang , Adrian Sandu

This paper is devoted to the construction of structure preserving stochastic Galerkin schemes for Fokker-Planck type equations with uncertainties and interacting with an external distribution, that we refer to as a background distribution.…

Numerical Analysis · Mathematics 2019-07-30 Mattia Zanella

In uncertainty quantification, a stochastic modelling is often applied, where parameters are substituted by random variables. We investigate linear dynamical systems of ordinary differential equations with a quantity of interest as output.…

Numerical Analysis · Mathematics 2019-09-23 Roland Pulch , Akil Narayan

We consider the development of high order space and time numerical methods based on Implicit-Explicit (IMEX) multistep time integrators for hyperbolic systems with relaxation. More specifically, we consider hyperbolic balance laws in which…

Numerical Analysis · Mathematics 2020-01-14 Giacomo Albi , Giacomo Dimarco , Lorenzo Pareschi