| |
Gauss–Runge–Kutta time discretization of wave equations on evolving surfaces
- 作者：Dhia Mansour
- 关键词：65M12 ; 65M15 ; 65M60 ; 35L99 ; 35R01 ; 35R37
- 刊名：Numerische Mathematik
- 出版年：2015
- 出版时间：January 2015
- 年：2015
- 卷：129
- 期：1
- 页码：21-53
- 全文大小：896 KB
- 参考文献：1. Bastian, P., Blatt, M., Dedner, A., Engwer, C., Fahlke, J., Gr?ser, C., Kl?fkorn, R., Nolte, M., Ohlberger, M., Sander, O. (2013) http://www.dune-project.org
2. Burrage, K., Hundsdorfer, W.H., Verwer, J.G.: A study of B-convergence of Runge–Kutta methods. Computing 36(1), 17-4 (1986) CrossRef
3. Deckelnick, K., Elliott, C., Styles, V.: Numerical diffusion-induced grain boundary motion. Interfaces Free Bound. 3, 393-14 (2001) CrossRef
4. Dekker, K., Kraaijevanger, J.F.B.M., Spijker, M.N.: The order of B-convergence of the Gaussian Runge–Kutta method. Computing 36(1), 35-1 (1986) CrossRef
5. Dedner, A., Kl?fkorn, R., Nolte, M., Ohlberger, M.: A generic interface for parallel and adaptive scientific computing: abstraction principles and the DUNE-FEM module. Computing 90, 165-96 (2010) CrossRef
6. Dedner, A., Kl?fkorn, R., Nolte, M., Ohlberger, M. (2013) http://dune.mathematik.uni-freiburg.de
7. Dziuk, G., Elliott, C.M.: Finite elements on evolving surfaces. IMA J. Numer. Anal. 27, 262-92 (2007) CrossRef
8. Dziuk, G., Elliott, C.M.: \(L^2\) -estimates for the evolving surface finite element method. Math. Comp. 82, 1-4 (2013) CrossRef
9. Dziuk, G., Elliott, C.M.: A fully discrete evolving surface finite element method., vol. 50, No. 5, pp. 2677-694. ISSN 1095-170 (2012)
10. Dziuk, G., Elliott, C.M.: SIAM J. Numer. Anal. 50(5), 2677-694 (2012) CrossRef
11. Dziuk, G., Lubich, C., Mansour, D.: Runge–Kutta time discretization of parabolic differential equations on evolving surfaces. IMA J. Numer. Anal. 32, 394-16 (2012) CrossRef
12. Gilbarg, D., Trudinger, N.S.: Elliptic Partial Differential Equations of Second Order, 2nd edn. Springer, Berlin (1983) CrossRef
13. Hairer, E., Lubich, C., Wanner, G.: Geometric numerical integration. In: Structure-Preserving Algorithms for Ordinary Differential Equations. 2nd ed. Springer, Berlin (2006)
14. Hairer, E., N?rsett, S.P., Wanner, G.: Solving Ordinary Differential Equations. I. Nonstiff Problems, 2nd edn. Springer, Berlin (1993)
15. Hairer, E., Wanner, G.: Solving Ordinary Differential Equations. II. Stiff and differential-algebraic problems, 2nd edn. Springer, Berlin (1996) CrossRef
16. Halpern, D., Jenson, O.E., Grotberg, J.B.: A theoretical study of surfactant and liquid delivery into the lung. J. Appl. Physiol. 85, 333-52 (1998)
17. James, A., Lowengrub, J.: A surfactant-conserving volume-of-fluid method for interfacial flows with insoluble surfactant. J. Comp. Phys. 201, 685-22 (2004) CrossRef
18. Kraaijevanger, J.F.B.M.: B-convergence of the implicit midpoint rule and the trapezoidal rule. BIT Numer. Math. 25(4), 652-66 (1985) CrossRef
19. Lenz, M., Nemadjieu, S.F., Rumpf, M.: A convergent finite volume scheme for diffusion on evolving surfaces. SIAM J. Numer. Anal. 49(1), 15-7 (2011)
文摘
This paper is concerned with an error analysis for a full discretization of the linear wave equation on a moving surface. The equation is discretized in space by the evolving surface finite element method. Discretization in time is done by Gau?–Runge–Kutta (GRK) methods, aiming for higher-order accuracy in time and unconditional stability of the fully discrete scheme. The latter is established in the natural time-dependent norms by using the algebraic stability and the coercivity property of the GRK methods together with the properties of the spatial semi-discretization. Under sufficient regularity conditions, optimal-order error estimates for this class of fully discrete methods are shown. Numerical experiments are presented to confirm some of the theoretical results.
| |
NGLC 2004-2010.National Geological Library of China All Rights Reserved.
Add:29 Xueyuan Rd,Haidian District,Beijing,PRC. Mail Add: 8324 mailbox 100083
For exchange or info please contact us via email.
| |
