A finite difference moving mesh method based on conservation for moving boundary problems

Journal of Computational and Applied Mathematics

Volumn 288, Issue , 2015, Pages 1-17

  Lee, T E ^a,b   Baines, M J ^a   Langdon, S ^a  

^a UNIVERSITY OF READING   (United Kingdom)

^b UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Finite difference methods; Mass conservation; Time dependent partial differential equations; Velocity based moving meshes

Indexed keywords

DIFFERENTIAL EQUATIONS; POROUS MATERIALS;

INTEGRAL APPROACH; MASS CONSERVATION; MOVING BOUNDARY PROBLEMS; MOVING MESH; MOVING MESH METHOD; POROUS MEDIUM EQUATION; RICHARDS 'EQUATION; TIME-DEPENDENT PARTIAL DIFFERENTIAL EQUATIONS;

FINITE DIFFERENCE METHOD;

EID: 84928479321     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2015.03.032     Document Type: Article

References (26)

1. C. Budd, W. Huang, and R.D. Russell Adaptivity with moving grids Acta Numer. 2009 111 241
2. W. Huang, and R.D. Russell Adaptive Moving Mesh Methods 2011 Springer New York
3. G. Beckett, J.A. Mackenzie, and M.L. Robertson A moving mesh finite element method for the solution of two-dimensional Stefan problems J. Comput. Phys. 168 2001 500 518
4. W. Huang, Y. Ren, and R.D. Russell Moving mesh partial differential equations (MMPDEs) based on the equidistribution principle SIAM J. Sci. Comput. 31 1994 709 730
5. K. Miller, and R.N. Miller Moving finite elements. I SIAM J. Numer. Anal. 18 1981 1019 1032
6. K. Miller Moving finite elements. II SIAM J. Numer. Anal. 18 1981 1033 1057
7. C.J. Budd, and J.F. Williams Parabolic Monge-Ampere methods for blow-up problems in several spatial dimensions J. Phys. A 39 2006 5425 5444
8. C.J. Budd, and J.F. Williams Moving mesh generation using the parabolic Monge-Ampere equation SIAM J. Sci. Comput. 2008
9. M.J. Baines, M.E. Hubbard, and P.K. Jimack A moving mesh finite element algorithm for the adaptive solution of time-dependent partial differential equations with moving boundaries Appl. Numer. Math. 54 2005 450 469
10. M.J. Baines, M.E. Hubbard, and P.K. Jimack Velocity-based moving mesh methods for nonlinear partial differential equations Commun. Comput. Phys. 10 2011 509 576
11. G. Liao, and D. Anderson A new approach to grid generation Appl. Anal. 44 1992 285 298
12. G. Liao, and J. Xue Moving meshes by the deformation method J. Comput. Appl. Math. 195 2006 83 92
13. W. Cao, W. Huang, and R.D. Russell A moving-mesh method based on the geometric conservation law SIAM J. Sci. Comput. 24 2002 118 142
14. T.E. Lee, M.J. Baines, S. Langdon, and M.J. Tindall A moving mesh approach for modelling avascular tumour growth Appl. Numer. Math. 72 2013 99 114
15. J.L. Vazquez The Porous Medium Equation: Mathematical Theory 2007 Oxford University Press
16. L.A. Richards Capillary conduction of liquids through porous mediums Physics 1 5 1931 318 333
17. J. Crank, and R.S. Gupta A moving boundary problem arising from the diffusion of oxygen in absorbing tissue J. Inst. Math. Appl. 10 1972 19 33
18. J. Parker An invariant approach to moving-mesh methods for PDEs (M.Sc. dissertation) 2010 Brasenose College, University of Oxford UK
19. J.N. Dewynne, S.D. Howison, I. Rupf, and P. Wilmott Some mathematical results in the pricing of American options European J. Appl. Math. 4 1993 381 398
20. H.O. Dahmardah, and D.F. Mayers A Fourier-series solution of the Crank-Gupta equation IMA J. Numer. Anal. 3 1983 81 85
21. G.I. Barenblatt On some unsteady motions of fluids and gases in a porous medium Prikl. Mat. Mekh. 6 1952 67 78 (Translated in J. Appl. Math. Mech.)
22. R.E. Pattle Diffusion from an instantaneous point source with a concentration-dependent coefficient Quart. J. Mech. Appl. Math. 12 1959 407 409
23. R.O. Moody, and M.J. Baines A constrained moving finite element solution of the one-dimensional oxygen diffusion with absorption problem J. Comput. Phys. 103 2 1992 442 449
24. E. Hansen, and P. Hougaard On a moving boundary problem with biomechanics H. Inst. Math. Appl. 13 1974 385 398
25. M.J. Baines, and T.E. Lee A large time-step implicit moving mesh scheme for moving boundary problems Numer. Methods Partial Differential Equations 30 2014 321 338
26. G. Scherer, and M.J. Baines Moving mesh finite difference schemes for the porous medium equation, Mathematics Report Series 1/2012 2012 Department of Mathematics and Statistics, University of Reading UK