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The High-Order Variable-Coefficient Explicit-Implicit-Null Method for Diffusion and Dispersion Equations 认领 引用
1
作者 Meiqi Tan Juan Cheng Chi-Wang Shu 《Communications on Applied Mathematics and Computation》 EI CSCD 2025年第1期115-150,共36页
For the high-order diffusion and dispersion equations, the general practice of the explicit-implicit-null (EIN) method is to add and subtract an appropriately large linear highest derivative term with a constant coeff... For the high-order diffusion and dispersion equations, the general practice of the explicit-implicit-null (EIN) method is to add and subtract an appropriately large linear highest derivative term with a constant coefficient at one side of the equation, and then apply the standard implicit-explicit method to the equivalent equation. We call this approach the constant-coefficient EIN method in this paper and hereafter denote it by “CC-EIN”. To reduce the error in the CC-EIN method, the variable-coefficient explicit-implicit-null (VC-EIN) method, which is obtained by adding and subtracting a linear highest derivative term with a variable coefficient, is proposed and studied in this paper. Coupled with the local discontinuous Galerkin (LDG) spatial discretization, the VC-EIN method is shown to be unconditionally stable and can achieve high order of accuracy for both one-dimensional and two-dimensional quasi-linear and nonlinear equations. In addition, although the computational cost slightly increases, the VC-EIN method can obtain more accurate results than the CC-EIN method, if the diffusion coefficient or the dispersion coefficient has a few high and narrow bumps and the bumps only account for a small part of the whole computational domain. 展开更多
关键词 Diffusion equation Dispersion equation Stability Explicit-implicit-null(EIN)time discretization Local discontinuous Galerkin(LDG)method
Local discontinuous Galerkin methods with explicit-implicit-null time discretizations for solving nonlinear diffusion problems 认领 引用 被引量：6
2
作者 Haijin Wang Qiang Zhang +1 位作者 Shiping Wang Chi-Wang Shu 《Science China Mathematics》 SCIE CSCD 2020年第1期183-204,共22页
In this paper,we discuss the local discontinuous Galerkin methods coupled with two specific explicitimplicit-null time discretizations for solving one-dimensional nonlinear diffusion problems Ut=(a(U)Ux)x.The basic id... In this paper,we discuss the local discontinuous Galerkin methods coupled with two specific explicitimplicit-null time discretizations for solving one-dimensional nonlinear diffusion problems Ut=(a(U)Ux)x.The basic idea is to add and subtract two equal terms a0 Uxx the right-hand side of the partial differential equation,then to treat the term a0 Uxx implicitly and the other terms(a(U)Ux)x-a0 Uxx explicitly.We give stability analysis for the method on a simplified model by the aid of energy analysis,which gives a guidance for the choice of a0,i.e.,a0≥max{a(u)}/2 to ensure the unconditional stability of the first order and second order schemes.The optimal error estimate is also derived for the simplified model,and numerical experiments are given to demonstrate the stability,accuracy and performance of the schemes for nonlinear diffusion equations. 展开更多
关键词 local discontinuous Galerkin explicit-implicit-null time discretization nonlinear diffusion stability error estimates
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