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• W2005728335 abstract "In this paper, we show how to accurately estimate the local truncation error of partial differential equations in a quasi-a priori way. We approximate the spatial truncation error using the @t-estimation procedure, which aims to compare the discretisation on a sequence of grids with different spacing. While most of the works in the literature focused on an a posteriori estimation, the following work develops an estimator for non-converged solutions. First, we focus the analysis on one- and two-dimensional scalar non-linear test cases to examine the accuracy of the approach using a finite difference discretisation. Then, we extend the analysis to a two-dimensional vectorial problem: the Euler equations discretised using a finite volume vertex-based approach. Finally, we propose to analyse a direct application: @t-extrapolation based on non-converged @t-estimation. We demonstrate that a solution with an improved accuracy can be obtained from a non-a posteriori error estimation approach." @default.
• W2005728335 created "2016-06-24" @default.
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• W2005728335 date "2013-11-01" @default.
• W2005728335 modified "2023-09-26" @default.
• W2005728335 title "Quasi-a priori truncation error estimation and higher order extrapolation for non-linear partial differential equations" @default.
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• W2005728335 doi "https://doi.org/10.1016/j.jcp.2013.07.018" @default.
• W2005728335 hasPublicationYear "2013" @default.
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