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An A Priori Error Analysis of the Local Discontinuous Galerkin Method for Elliptic Problems [PDF]
SIAM Journal on Numerical Analysis, 2000 In this paper, we present the first a priori error analysis for the local discontinuous Galerkin (LDG) method for a model elliptic problem. For arbitrary meshes with hanging nodes and elements of various shapes, we show that, for stabilization parameters
P. Castillo +3 more
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Superconvergence of the local discontinuous Galerkin method for nonlinear convection-diffusion problems [PDF]
Journal of Inequalities and Applications, 2017 In this paper, we discuss the superconvergence of the local discontinuous Galerkin methods for nonlinear convection-diffusion equations. We prove that the numerical solution is ( k + 3 / 2 ) $(k+3/2)$ th-order superconvergent to a particular projection ...
Hui Bi, Chengeng Qian
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An Optimized Schwarz Method for the Optical Response Model Discretized by HDG Method [PDF]
Entropy, 2023 An optimized Schwarz domain decomposition method (DDM) for solving the local optical response model (LORM) is proposed in this paper. We introduce a hybridizable discontinuous Galerkin (HDG) scheme for the discretization of such a model problem based on ...
Jia-Fen Chen +3 more
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A Local Discontinuous Galerkin Method for KdV Type Equations
SIAM Journal on Numerical Analysis, 2002 In this paper we develop a local discontinuous Galerkin method for solving KdV type equations containing third derivative terms in one and two space dimensions. The method is based on the framework of the discontinuous Galerkin method for conservation laws and the local discontinuous Galerkin method for viscous equations containing second derivatives ...
Chi-Wang Shu, Jue Yan
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Supercloseness of the local discontinuous Galerkin method for a singularly perturbed convection-diffusion problem [PDF]
Mathematics of Computation, 2022 A singularly perturbed convection-diffusion problem posed on the unit square in $\mathbb{R}^2$, whose solution has exponential boundary layers, is solved numerically using the local discontinuous Galerkin (LDG) method with piecewise polynomials of degree
Yao Cheng, Shan Jiang, M. Stynes
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An oscillation free local discontinuous Galerkin method for nonlinear degenerate parabolic equations [PDF]
Numerical Methods for Partial Differential Equations, 2021 An oscillation free local discontinuous Galerkin (OFLDG) method is proposed for solving nonlinear degenerate parabolic equations. The damping terms are added to the original LDG scheme to control the spurious oscillations when solutions have a large ...
Q. Tao +3 more
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Journal of Harbin University of Science and Technology, 2022 The equivalence between direct flux reconstruction method and discontinuous Galerkin method for solving parabolic equation and convection-diffusion equation is studied.
BI Hui, LIU Lei
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A discontinuous Galerkin method to solve Liouville’s equation of geometrical optics [PDF]
EPJ Web of Conferences, 2022 We present an alternative method to ray tracing that is based on a phase space description of light propagation. Liouville’s equation of geometrical optics describes the evolution of the basic luminance on phase space.
van Gestel Robert A.M. +3 more
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Local Discontinuous Galerkin Methods for the abcd Nonlinear Boussinesq System [PDF]
Communications on Applied Mathematics and Computation, 2021 Boussinesq type equations have been widely studied to model the surface water wave. In this paper, we consider the abcd Boussinesq system which is a family of Boussinesq type equations including many well-known models such as the classical Boussinesq system, BBM-BBM system, Bona-Smith system etc.
Jiawei Sun, Shusen Xie, Yulong Xing
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Axioms, 2023 For the purpose of solving elliptic partial differential equations, we suggest a new approach using an h-adaptive local discontinuous Galerkin approximation based on Sinc points.
Omar A. Khalil, Gerd Baumann
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