A Crank-Nicolson Type Space-Time Finite Element Method for Computing on Moving Meshes

Journal of Computational Physics

Volumn 159, Issue 2, 2000, Pages 274-289

  Hansbo, Peter ^a  

^a CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

Crank Nicolson; Method of characteristics; Space time finite element

Indexed keywords

CONVECTION-DOMINATED PROBLEMS; CRANK-NICOLSON; EVOLUTION PROBLEM; METHOD OF CHARACTERISTICS; MOVING MESH; SECOND ORDERS; SPACE AND TIME; SPACE TIME FINITE ELEMENT; SPACE-TIME FINITE ELEMENT METHOD; SPACETIME;

FINITE ELEMENT METHOD;

EID: 0347699575     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.2000.6436     Document Type: Article

References (20)

1. A. K. Aziz and P. Monk, Continuous finite elements in space and time for the heat equation, Math. Comp. 52, 255 (1989).
2. R. Bonnerot and P. Jamet, A second order finite element method for the one-dimensional Stefan problem, Int. J. Numer. Methods Eng. 8, 811 (1974).
3. R. Bonnerot and P. Jamet, Numerical computation of the free boundary for the two-dimensional Stefan problem by space-time elements, J. Comput. Phys. 25, 163 (1977).
4. J. Côté and A. Staniforth, A two time-level semi-Lagrangian semi-implicit scheme for spectral models, Mon. Weather Rev. 116, 2003-2012 (1988).
5. K. Eriksson, D. Estep, P. Hansbo, and C. Johnson, Computational Differential Equations (Cambridge Univ. Press, Cambridge, UK, 1996).
6. P. Hansbo, The characteristic streamline diffusion method for convection-diffusion problems, Comput. Methods Appl. Mech. Eng. 96, 239 (1992).
7. P. Hansbo, The characteristic streamline diffusion method for the time-dependent incompressible Navier-Stokes equations, Comput. Methods Appl. Mech. Eng. 99, 171 (1992).
8. P. Hansbo, Lagrangian incompressible flow computations in three dimensions by use of space-time finite elements, Int. J. Numer. Methods Fluids 20, 989 (1995).
9. P. Hansbo, Moving finite element methods by use of space-time elements. I. Scalar problems, Numer. Methods Partial Differ. Eq. 14, 251 (1998).
10. Y. Hasbani, E. Livne, and M. Bercovier, Finite elements and characteristics applied to advection-diffusion equations, Comput. Fluids 11, 71 (1983).
11. B. L. Hulme, One-step piecewise polynomial Galerkin methods for initial value problems, Math. Comput. 26, 415 (1972).
12. P. Jamet, Galerkin-type approximations which are discontinuous in time for parabolic problems on a variable domain, SIAM J. Numer. Anal. 15, 912 (1978).
13. P. Jamet, Stability and convergence of a generalized Crank-Nicolson scheme on a variable mesh for the heat equation, SIAM J. Numer. Anal. 17, 530 (1980).
14. C. Johnson, A new approach to algorithms for convection problems which are based on exact transport + projection, Comput. Methods Appl. Mech. Eng. 100, 45 (1992).
15. K. W. Morton, Generalised Galerkin methods for hyperbolic problems, Comput. Methods Appl. Mech. Eng. 52, 847 (1985).
16. O. Pironneau, On the transport-diffusion algorithm and its application to the Navier-Stokes equations, Numer. Math. 38, 309 (1982).
17. O. Pironneau, J. Liou, and T. E. Tezduyar, Characteristic Galerkin and Galerkin/least-aquares space-time formulations for the advection-diffusion equation with time-dependent domains, Comput. Methods Appl. Mech. Eng. 100, 117 (1992).
18. T. E. Tezduyar, M. Behr, and J. Liou, A new strategy for finite element computations involving moving boundaries and interfaces - The deforming-spatial-domain/space-time procedure. I. The concept and the preliminary numerical tests, Comput. Methods Appl. Mech. Eng. 94, 339 (1992).
19. R. Winther, A stable finite element method for initial-boundary value problems for first order hyperbolic systems, Math. Comp. 36, 45 (1981).
20. O. C. Zienkiewicz, The Finite Element Method (McGraw-Hill, London, 1977), 3rd ed.