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Journal of Scientific Computing

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01-09-2018

Local Discontinuous Galerkin Methods with Generalized Alternating Numerical Fluxes for Two-dimensional Linear Sobolev Equation

Authors: Di Zhao, Qiang Zhang

Published in: Journal of Scientific Computing | Issue 3/2019

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Abstract

In this paper we present an efficient and high-order numerical method to solve two-dimensional linear Sobolev equations, which is based on the local discontinuous Galerkin (LDG) method with the upwind-biased fluxes and generalized alternating fluxes. A weak stability is given for both schemes, and a strong stability is established if the initial solutions exactly satisfy the elemental discontinuous Galerkin discretization. Moreover, the sharp error estimate in \(L^2\)-norm is established, by an elaborate application of the generalized Gauss–Radau projection. A fully-discrete LDG scheme is also considered, where the third-order explicit TVD Runge–Kutta algorithm is adopted. Finally some numerical experiments are given.

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Title: Local Discontinuous Galerkin Methods with Generalized Alternating Numerical Fluxes for Two-dimensional Linear Sobolev Equation
Authors: Di Zhao
Qiang Zhang
Publication date: 01-09-2018
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 3/2019
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-018-0819-2

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