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Published in:
2021 | OriginalPaper | Chapter
Time-Dependent Two-Dimensional Fourth-Order Problems: Optimal Convergence
Authors : J. -P. Croisille, D. Fishelov
Published in: Numerical Mathematics and Advanced Applications ENUMATH 2019
Publisher: Springer International Publishing
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Abstract
Here we present a new approach for the analysis of high-order compact schemes for the clamped plate problem. A similar model is the Navier-Stokes equation in streamfunction formulation. In our book “Navier-Stokes Equations in Planar Domains”, Imperial College Press, 2013, we have suggested fourth-order compact schemes for the Navier-Stokes equations. The same type of schemes may be applied to the clamped plate problem. For these methods the truncation error is only of first-order at near-boundary points, but is of fourth order at interior points. It is proven that the rate of convergence is actually four, thus the error tends to zero as O(h
4).