A Space-Time Trefftz Discontinuous Galerkin Method for the Linear Schrödinger Equation [PDF]
SIAM Journal on Numerical Analysis, 2021 A space-time Trefftz discontinuous Galerkin method for the Schr\"odinger equation with piecewise-constant potential is proposed and analyzed. Following the spirit of Trefftz methods, trial and test spaces are spanned by non-polynomial complex wave ...
S. G'omez, A. Moiola
semanticscholar +1 more source
Multigrid optimization for space-time discontinuous Galerkin discretizations of advection dominated flows [PDF]
, 2010 The goal of this research is to optimize multigrid methods for higher order accurate space-time discontinuous Galerkin discretizations. The main analysis tool is discrete Fourier analysis of two- and three-level multigrid algorithms.
A. Brandt +7 more
core +4 more sources
Spectral semi-implicit and space-time discontinuous Galerkin methods for the incompressible Navier-Stokes equations on staggered Cartesian grids [PDF]
, 2016 In this paper two new families of arbitrary high order accurate spectral discontinuous Galerkin (DG) finite element methods are derived on staggered Cartesian grids for the solution of the incompressible Navier-Stokes (NS) equations in two and three ...
F. Fambri, M. Dumbser
semanticscholar +1 more source
Algorithms and Data Structures for Multi-Adaptive Time-Stepping [PDF]
, 2008 Multi-adaptive Galerkin methods are extensions of the standard continuous and discontinuous Galerkin methods for the numerical solution of initial value problems for ordinary or partial differential equations.
Jansson, Johan, Logg, Anders
core +2 more sources
Space-Time Discontinuous Petrov–Galerkin Methods for Linear Wave Equations in Heterogeneous Media
Comput. Methods Appl. Math., 2019 We establish an abstract space-time DPG framework for the approximation of linear waves in heterogeneous media. The estimates are based on a suitable variational setting in the energy space.
Johannes Ernesti, C. Wieners
semanticscholar +1 more source
SPACE-TIME FINITE ELEMENT FORMULATION FOR SHALLOW WATER EQUATIONS WITH SHOCK-CAPTURING OPERATOR
Pesquimat, 2014 This paper presents a space-time formulation for problems governed by the shallow water equations. A linear time discontinuous approximation is adopted and the streamline upwind Petrov-Galerkin (SUPG) methodis applied in its equivalent form to fit the ...
Rigoberto G Sanabria Castro
doaj +1 more source
Implicit-explicit Runge–Kutta schemes and finite elements with symmetric stabilization for advection-diffusion equations [PDF]
, 2012 We analyze a two-stage implicit-explicit Runge–Kutta scheme for time discretization of advection-diffusion equations. Space discretization uses continuous, piecewise affine finite elements with interelement gradient jump penalty; discontinuous Galerkin ...
Burman, Erik, Ern, Alexandre
core +1 more source
Abstract and Applied Analysis, 2014 We propose, analyze, and test a fully discrete local discontinuous Galerkin (LDG) finite element method for a time-fractional diffusion equation. The proposed method is based on a finite difference scheme in time and local discontinuous Galerkin methods ...
Leilei Wei, Xindong Zhang
doaj +1 more source
IMA Journal of Numerical Analysis, 2019 We consider the $\varepsilon $-dependent stochastic Allen–Cahn equation with mild space–time noise posed on a bounded domain of $\mathbb{R}^2$. The positive parameter $\varepsilon $ is a measure for the inner layers width that are generated during ...
D. Antonopoulou
semanticscholar +1 more source
Penyelesaian Numerik Advection Equation 1 Dimensi dengan EFG-DGM
Media Komunikasi Teknik Sipil, 2016 Differential equation can be used to model various phenomena in science and engineering. Numerical method is the most common method used in solving DE.
Kresno Wikan Sadono
doaj +1 more source