Abstract
The purpose of this work is to verify the asymptotic order of the discretization error of two one-dimensional problems modeled by the advection-diffusion and Burgers equations. The problems are solved using first and second-order accurate spatial approximations, with and without mixing (hybrid scheme), by deferred correction. It was verified that the accuracy of hybrid schemes is equal to that of the lowest-order pure scheme.
Highlights
Accurate and reliable numerical solutions depend on the estimation of the numerical error (E), which can be defined as the difference between the exact analytical solution (Φ) of a variable of interest and its numerical solution (φ), i.e., E(φ) = Φ – φ
When the other sources do not exist or are very small compared to thetruncation error, E can be called by discretization error
A numerical solution is obtained because the analytical solution isunknown
Summary
Accurate and reliable numerical solutions depend on the estimation of the numerical error (E), which can be defined as the difference between the exact analytical solution (Φ) of a variable of interest and its numerical solution (φ), i.e., E(φ) = Φ – φ (1). Where E is caused by four sources of error [1]: truncation, iteration, round-off andprogramming. When the other sources do not exist or are very small compared to thetruncation error, E can be called by discretization error. A numerical solution is obtained because the analytical solution isunknown. The true value of the numerical error is unknown and must beestimated. There are two estimators for the discretization error that are widely used with themethods of finite difference and finite volume, both of them based on Richardsonextrapolation. One of them is Richardson estimator, which is given by [2]
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