Results 1 to 10 of about 102,481 (112)
Embedded Trefftz discontinuous Galerkin methods [PDF]
International Journal for Numerical Methods in Engineering, 2022 In 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.
C. Lehrenfeld, P. Stocker
semanticscholar +6 more sources
Discontinuous Galerkin methods [PDF]
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2003 This paper is a short essay on discontinuous Galerkin methods intended for a very wide audience. We present the discontinuous Galerkin methods and describe and discuss their main features.
Bernardo Cockburn
semanticscholar +2 more sources
Local Randomized Neural Networks with Discontinuous Galerkin Methods for Partial Differential Equations [PDF]
Journal of Computational and Applied Mathematics, 2022 Randomized neural networks (RNN) are a variation of neural networks in which the hidden-layer parameters are fixed to randomly assigned values and the output-layer parameters are obtained by solving a linear system by least squares.
Jingbo Sun, S. Dong, Fei Wang
semanticscholar +1 more source
Sparse invariant domain preserving discontinuous Galerkin methods with subcell convex limiting [PDF]
Computer Methods in Applied Mechanics and Engineering, 2020 In this paper, we develop high-order nodal discontinuous Galerkin (DG) methods for hyperbolic conservation laws that satisfy invariant domain preserving properties using a subcell flux corrections and convex limiting. These methods are based on a subcell
Will Pazner
semanticscholar +1 more source
A Neural Network based Shock Detection and Localization Approach for Discontinuous Galerkin Methods [PDF]
Journal of Computational Physics, 2020 The stable and accurate approximation of discontinuities such as shocks on a finite computational mesh is a challenging task. Detection of shocks or strong discontinuities in the flow solution is typically achieved through a priori troubled cell ...
A. Beck +3 more
semanticscholar +1 more source
A multilevel discontinuous Galerkin method [PDF]
Numerische Mathematik, 2003 With extended references to the major papers on the subject, this work analyzes mathematically multigrid techniques for two discontinuous Galerkin methods: one for elliptic problems and a second one for singular perturbed advection-diffusion problems. In the former case, the analysis predicts convergence rates of the multigrid method independent of the
Jay Gopalakrishnan, Guido Kanschat
openaire +4 more sources
Nonlinear discontinuous Petrov–Galerkin methods [PDF]
Numerische Mathematik, 2018 The discontinuous Petrov-Galerkin method is a minimal residual method with broken test spaces and is introduced for a nonlinear model problem in this paper. Its lowest-order version applies to a nonlinear uniformly convex model example and is equivalently characterized as a mixed formulation, a reduced formulation, and a weighted nonlinear least ...
Carsten Carstensen +3 more
openaire +2 more sources
On discretely entropy conservative and entropy stable discontinuous Galerkin methods [PDF]
Journal of Computational Physics, 2017 High order methods based on diagonal-norm summation by parts operators can be shown to satisfy a discrete conservation or dissipation of entropy for nonlinear systems of hyperbolic PDEs [1] , [2] .
J. Chan
semanticscholar +1 more source
Convergence of a Discontinuous Galerkin Multiscale Method [PDF]
SIAM Journal on Numerical Analysis, 2013 A convergence result for a discontinuous Galerkin multiscale method for a second order elliptic problem is presented. We consider a heterogeneous and highly varying diffusion coefficient in $L^\infty(Ω,\mathbb{R}^{d\times d}_{sym})$ with uniform spectral bounds and without any assumption on scale separation or periodicity.
Daniel Elfverson +3 more
openaire +3 more sources
hp-Version discontinuous Galerkin methods on essentially arbitrarily-shaped elements [PDF]
Mathematics of Computation, 2019 We extend the applicability of the popular interior-penalty discontinuous Galerkin (dG) method discretizing advection-diffusion-reaction problems to meshes comprising extremely general, essentially arbitrarily-shaped element shapes.
A. Cangiani +2 more
semanticscholar +1 more source