Truncation error analysis of the finite volume method for a model steady convective equation
Journal of Computational Physics
SIAM Journal on Scientific Computing
Journal of Computational Physics
Multigrid
Review of code and solution verification procedures for computational simulation
Journal of Computational Physics
A priori mesh quality estimation via direct relation between truncation error and mesh distortion
Journal of Computational Physics
Verification and Validation in Scientific Computing
Verification and Validation in Scientific Computing
The Estimation of Truncation Error by $$\tau $$-Estimation for Chebyshev Spectral Collocation Method
Journal of Scientific Computing
Hi-index | 31.45 |
The aim of this paper was to accurately estimate the local truncation error of partial differential equations, that are numerically solved using a finite difference or finite volume approach on structured and unstructured meshes. In this work, we approximated the local truncation error using the @t-estimation procedure, which aims to compare the residuals on a sequence of grids with different spacing. First, we focused the analysis on one-dimensional scalar linear and non-linear test cases to examine the accuracy of the estimation of the truncation error for both finite difference and finite volume approaches on different grid topologies. Then, we extended the analysis to two-dimensional problems: first on linear and non-linear scalar equations and finally on the Euler equations. We demonstrated that this approach yields a highly accurate estimation of the truncation error if some conditions are fulfilled. These conditions are related to the accuracy of the restriction operators, the choice of the boundary conditions, the distortion of the grids and the magnitude of the iteration error.