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).
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Acknowledgements
The authors would like thank Professor Matania Ben-Artzi from the Hebrew University, for his comments and insights concerning the matter of this work.
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Croisille, J.P., Fishelov, D. (2021). Time-Dependent Two-Dimensional Fourth-Order Problems: Optimal Convergence. In: Vermolen, F.J., Vuik, C. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2019. Lecture Notes in Computational Science and Engineering, vol 139. Springer, Cham. https://doi.org/10.1007/978-3-030-55874-1_42
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DOI: https://doi.org/10.1007/978-3-030-55874-1_42
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