Results 11 to 20 of about 752 (185)
Well-Balanced High-Order Discontinuous Galerkin Methods for Systems of Balance Laws
Mathematics, 2021 This work introduces a general strategy to develop well-balanced high-order Discontinuous Galerkin (DG) numerical schemes for systems of balance laws.
Ernesto Guerrero Fernández +2 more
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The Discontinuous Galerkin Method with Diffusion [PDF]
Mathematics of Computation, 1992 Let \(\Omega\subset \mathbb{R}^ 2\) be a bounded polygon and \(\alpha=(\alpha_ 1,\alpha_ 2)\) a unit vector. The author considers the following class of constant-coefficient convection-diffusion equations: (1) \(u_ \alpha-\sigma_ 1u_{xx}-\sigma_ 2u_{yy}=f\), where \((x,y)\in \Omega\), \(u_ \alpha=\alpha\cdot\bigtriangledown u\) and \(\sigma_ 1\) and \(\
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Advanced Modeling and Simulation in Engineering Sciences, 2019 This research work presents some comparisons and analyses of the time discontinuous space–time Galerkin method and the space discontinuous Galerkin method applied to elastic wave propagation in anisotropic and heterogeneous media.
Bing Tie
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Convergence of the Discontinuous Galerkin Method for Discontinuous Solutions [PDF]
SIAM Journal on Numerical Analysis, 2005 The author proves convergence of a discontinuous Galerkin method for a convection-reaction equation under very weak assumptions on the coefficients. The proof is based on work of \textit{R. J. DiPerna} and \textit{P. L. Lions} [Invent. Math. 98, 511--547 (1989; Zbl 0696.34049)]. Applications include modeling the flow of incompressible immiscible fluids.
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Steady-State Simulation of Semiconductor Devices Using Discontinuous Galerkin Methods
IEEE Access, 2020 Design of modern nanostructured semiconductor devices often calls for simulation tools capable of modeling arbitrarily-shaped multiscale geometries. In this work, to this end, a discontinuous Galerkin (DG) method-based framework is developed to simulate ...
Liang Chen, Hakan Bagci
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Quail: A lightweight open-source discontinuous Galerkin code in Python for teaching and prototyping
SoftwareX, 2022 In this paper, we present Quail, a lightweight discontinuous Galerkin solver written in Python. The aim of this code is to serve not only as a teaching tool for newcomers to the rapidly growing field, but also as a prototyping platform for testing ...
Eric J. Ching +3 more
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Journal of Inequalities and Applications, 2010 We analyze discontinuous Galerkin methods with penalty terms, namely, symmetric interior penalty Galerkin methods, to solve nonlinear Sobolev equations.
Hyun Young Lee +2 more
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Error Estimates for Local Discontinuous Galerkin Methods for Linear Fourth-order Equations
Journal of Harbin University of Science and Technology, 2021 This paper studies the stability and error estimates of the local discontinuous Galerkin method for fourth-order linear partial differential equations based on upwind-biased fluxes. Consider using the semi-discrete form of numerical format in the spatial
BI Hui, CHEN Sha-sha
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Comparison of the stability of discontinuous Galerkin and finite-difference methods
Lietuvos Matematikos Rinkinys, 2002 In this article we present stability analysis of two discrete schemes, which are used to solve a parabolic problem on adaptive nonstationary meshes. The influence of interpolation and projection errors is investigated.
Raimondas Čiegis +2 more
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Mathematical Modelling and Analysis, 2012 In this paper we develop and analyze an implicit fully discrete local discontinuous Galerkin (LDG) finite element method for a time-fractional Zakharov–Kuznetsov equation.
Zongxiu Ren +3 more
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