Results 31 to 40 of about 8,904 (236)

Convergence of adaptive discontinuous Galerkin methods

Mathematics of Computation, 2018
We develop a general convergence theory for adaptive discontinuous Galerkin methods for elliptic PDEs covering the popular SIPG, NIPG and LDG schemes as well as all practically relevant marking strategies. Another key feature of the presented result is, that it holds for penalty parameters only necessary for the standard analysis ...
Christian Kreuzer, Emmanuil H. Georgoulis   +1 more
openaire   +3 more sources

A Computational Study of an Implicit Local Discontinuous Galerkin Method for Time-Fractional Diffusion Equations

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

Direct discontinuous Galerkin method for potential magnetic field solutions

Frontiers in Astronomy and Space Sciences, 2022
In this paper, we employ the direct discontinuous Galerkin (DDG) method for the first time to extrapolate the coronal potential magnetic field (PF) with the source surface (SS) and call the developed numerical model as the DDG-PFSS solver. In this solver,
XiaoJing Liu, Xueshang Feng, Xueshang Feng, Xueshang Feng, Jiakun Lv, Jiakun Lv, Xinyi Wang, Xinyi Wang, Man Zhang   +8 more
doaj   +1 more source

Embedded Trefftz discontinuous Galerkin methods

International Journal for Numerical Methods in Engineering, 2023
AbstractIn Trefftz discontinuous Galerkin methods a partial differential equation is discretized using discontinuous shape functions that are chosen to be elementwise in the kernel of the corresponding differential operator. We propose a new variant, the embedded Trefftz discontinuous Galerkin method, which is the Galerkin projection of an underlying ...
Christoph Lehrenfeld, Paul Stocker
openaire   +4 more sources

Discontinuous Galerkin methods for the biharmonic problem [PDF]

IMA Journal of Numerical Analysis, 2008
This work is concerned with the design and analysis of hp-version discontinuous Galerkin (DG) finite element methods for boundary-value problems involving the biharmonic operator. The first part extends the unified approach of Arnold, Brezzi, Cockburn & Marini (SIAM J. Numer. Anal.
Georgoulis, EH, Houston, P
openaire   +3 more sources

Discontinuous Galerkin Methods for the Ostrovsky–Vakhnenko Equation [PDF]

Journal of Scientific Computing, 2020
In this paper, we develop discontinuous Galerkin (DG) methods for the Ostrovsky-Vakhnenko (OV) equation, which yields the shock solutions and singular soliton solutions, such as peakon, cuspon and loop solitons. The OV equation has also been shown to have a bi-Hamiltonian structure.
Qian Zhang 0056, Yinhua Xia
openaire   +2 more sources

Computation of Trailing Edge Noise with a Discontinuous Galerkin Method

, 2010
Trailing edge noise of a semi-infinite, thin, flat plate situated in low Mach number flow is computed in two spatial dimensions. The Acoustic Perturbation Equations (APE), which are employed as governing equations, are discretized via a Discontinuous ...
M. Bauer, Bauer, Marcus
core   +1 more source

DEIP, discontinuous element insertion Program — Mesh generation for interfacial finite element modeling

SoftwareX, 2018
The Discontinuous Element Insertion Program is a MATLAB/Octave toolbox for inserting zero-thickness interface elements into two and three dimensional finite element meshes.
Timothy J. Truster
doaj   +1 more source

An Unfitted Discontinuous Galerkin Method for Elliptic Interface Problems

Journal of Applied Mathematics, 2014
An unfitted discontinuous Galerkin method is proposed for the elliptic interface problems. Based on a variant of the local discontinuous Galerkin method, we obtain the optimal convergence for the exact solution u in the energy norm and its flux p in the ...
Qiuliang Wang, Jinru Chen
doaj   +1 more source

Edge‐Based Discretizations on Triangulations in Any Dimension, With Special Attention to Four‐Dimensional Space

International Journal for Numerical Methods in Fluids, EarlyView.
This article provides important geometric formulas for node‐centered, edge‐based schemes in any number of dimensions. These formulas are noteworthy, as they do not require the explicit formation of dual regions. We prove several key geometric results, with a particular focus on the four‐dimensional case, due to potential space‐time applications ...
Nicholas Tufillaro, David M. Williams, Hiroaki Nishikawa   +2 more
wiley   +1 more source