Analysis of Flux Corrected Transport Schemes for Evolutionary Convection-Diffusion-Reaction Equations

一种用于对流-扩散-反应问题的初始修正分裂方法

An initial-corrected splitting approach for convection-diffusion-reaction problems

针对Dirichlet边界条件下对流-扩散-反应问题分裂方法的阶数降低问题，提出初始修正分裂方法，经分析证明其为二阶收敛，并通过数值实验验证了性能。

Flux-corrected transport for scalar hyperbolic conservation laws and convection-diffusion equations by using linear programming

Flux-corrected transport (FCT) is one of the flux limiter methods. Unlike the total variation diminishing methods, obtaining the known FCT formulas for computing flux limiters is not quite transparent, and their transformation is not obvious when the original differential operator changes. We propose a novel formal mathematical approach to design flux correction for weighted hybrid difference schemes by using linear programming. The hybrid scheme is a linear combination of a monotone scheme and a high order scheme. The determination of maximal antidiffusive fluxes is treated as an optimization…

Optimal convergence rate of the explicit Euler method for convection-diffusion equations II: high dimensional cases

This is the second part of study on the optimal convergence rate of the explicit Euler discretization in time for the convection-diffusion equations [Appl. Math. Lett. \textbf{131} (2022) 108048] which focuses on high-dimensional linear/nonlinear cases under Dirichlet or Neumann boundary conditions. Several new corrected difference schemes are proposed based on the explicit Euler discretization in temporal derivative and central difference discretization in spatial derivatives. The priori estimate of the corrected scheme with application to constant convection coefficients is provided at lengt…

演化对流-扩散问题的非协调逼近的后验误差估计

A Posteriori Error Estimates for Nonconforming Approximations of Evolutionary Convection-Diffusion Problems

本文通过积分恒等式的变换，推导了演化对流-扩散问题精确解与近似解之间可计算的上界，该估计不依赖于解的特殊性质，仅涉及嵌入不等式中的全局常数，并讨论了分段连续逼近的扩展。

A note on the application of the Guermond-Pasquetti mass lumping correction technique for convection-diffusion problems

We provide a careful Fourier analysis of the Guermond-Pasquetti mass lumping correction technique [Guermond J.-L., Pasquetti R. A correction technique for the dispersive effects of mass lumping for transport problems. - Computer Methods in Applied Mechanics and Engineering. - 2013. - Vol. 253. - P. 186-198] applied to pure transport and convection-diffusion problems. In particular, it is found that increasing the number of corrections reduces the accuracy for problems with diffusion; however all the corrected schemes are more accurate than the consistent Galerkin formulation in this case. For …

对流-扩散-反应方程代数稳定离散化求解器的评估

An Assessment of Solvers for Algebraically Stabilized Discretizations of Convection-Diffusion-Reaction Equations

本文系统评估了三维对流主导输运问题中通量修正有限元离散的各类求解器，通过新定义的三维测试问题揭示了限制技术、时间离散和求解器选择对整体计算性能的影响。