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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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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.
Sun, Jiawei, Xie, Shusen, Xing, Yulong
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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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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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Residual based a posteriori error estimation for Dirichlet boundary control problems [PDF]
ESAIM: Proceedings and Surveys, 2021 We study a residual–based a posteriori error estimate for the solution of Dirichlet boundary control problem governed by a convection diffusion equation on a two dimensional convex polygonal domain, using the local discontinuous Galerkin (LDG) method ...
Yücel Hamdullah
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Local Discontinuous Galerkin Methods for the Stokes System [PDF]
SIAM Journal on Numerical Analysis, 2002 A discontinuous Galerkin method for the Stokes problem is introduced and analysed. A priori error estimates for velocity and pressure are derived, which are shown to be optimal, if proper polynomial approximations and stabilization parameters are used.
Cockburn, Bernardo +3 more
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On the Local Discontinuous Galerkin Method for Linear Elasticity [PDF]
Mathematical Problems in Engineering, 2010 Following Castillo et al. (2000) and Cockburn (2003), a general framework of constructing discontinuous Galerkin (DG) methods is developed for solving the linear elasticity problem. The numerical traces are determined in view of a discrete stability identity, leading to a class of stable DG methods. A particular method, called the LDG method for linear
Chen, Yuncheng +3 more
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Numerical approximation of time-fractional Burgers-type equation
Advances in Difference Equations, 2020 In this work, we analyze and test a local discontinuous Galerkin method for solving the Burgers-type equation. The proposed numerical method, which is high-order accurate, is based on a finite difference scheme in time and local discontinuous Galerkin ...
Miaomiao Yang
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