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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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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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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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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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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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Advances in Aerodynamics, 2022 In this paper, we present a mesh adaptation algorithm for the unsteady compressible Navier-Stokes equations under the framework of local discontinuous Galerkin methods coupled with implicit-explicit Runge-Kutta or spectral deferred correction time ...
Xiangyi Meng, Yan Xu
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Journal of Inequalities and Applications, 2022 In this paper, we study the error estimates of local discontinuous Galerkin methods based on the generalized numerical fluxes for the one-dimensional linear fifth order partial differential equations.
Hui Bi, Yixin Chen
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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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Generalized Multiscale Finite Element Method for Elastic Wave Propagation in the Frequency Domain
Computation, 2020 In this work, we consider elastic wave propagation in fractured media. The mathematical model is described by the Helmholtz problem related to wave propagation with specific interface conditions (Linear Slip Model, LSM) on the fracture in the frequency ...
Uygulana Gavrilieva +2 more
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