6. Application Examples for FD Methods and Error Analysis

This video is about treatment of boundary conditions in finite-difference methods, especially related to higher-order schemes. Error estimation and verification of the order of the method based on Richardson extrapolation and systematic grid refinement is another important topic. The rest of the video is about the results obtained using different finite-difference methods of 1st, 2nd, 3rd, and 4th order to solve one 1D and one 2D flow problem involving convection and diffusion of a generic scalar. It is demonstrated that all implemented schemes converge with expected order, and especially that, when approximations of different order are used for convection and diffusion terms, the overall convergence rate toward a grid-independent solution corresponds to the lowest order of the used approximations.
You can download this video, the transcript of its soundtrack, the PowerPoint presentation file, and other supplementary material (computer codes for solving steady-state 1D and 2D convection-diffusion problems) from this site:
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