Semi-discrete Time-Dependent Fourth-Order Problems on an Interval: Error Estimate
We present high-order compact schemes for fourth-order time-dependent problems, which are related to the “buckling plate” or the “clamping plate” problems. Given a mesh size h, we show that the truncation error is O(h 4) at interior points and O(h) at near-boundary points. In addition, the convergence of these schemes is analyzed. Although the truncation error is only of first-order at near-boundary points, we have proved that the error of these schemes converges to zero as h tends to zero at least as O(h 3. 5). Numerical results are performed and they calibrate the high-order accuracy of the schemes. It is shown that the numerical rate of convergence is actually four, thus the error tends to zero as O(h 4).
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- 2.M. Ben-Artzi, J-P. Croisille, D. Fishelov, Convergence of a compact scheme for the pure streamfunction formulation of the unsteady Navier–Stokes system. SIAM J. Numer. Anal. 44, 1997–2024 (2006)Google Scholar
- 5.D. Fishelov, M. Ben-Artzi, J-P. Croisille, Recent advances in the study of a fourth-order compact scheme for the one-dimensional biharmonic equation. J. Sci. Comput. 53, 55–70 (2012)Google Scholar