An assumed-gradient finite element method for the level set equation

International Journal for Numerical Methods in Engineering

Volumn 64, Issue 8, 2005, Pages 1009-1032

  Mourad, Hashem M ^a   Dolbow, John ^a   Garikipati, Krishna ^b  

^a Duke University   (United States)

^b UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Finite element; Level set method; Stabilization

Indexed keywords

FINITE DIFFERENCE METHOD; GALERKIN METHODS; ORDINARY DIFFERENTIAL EQUATIONS; SET THEORY;

FINITE-ELEMENT MESHES; LEVEL SET METHOD;

FINITE ELEMENT METHOD;

FINITE ELEMENT METHOD;

EID: 27544477772     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.1395     Document Type: Article

References (21)

1. Osher S, Sethian JA. Fronts propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulation. Journal of Computational Physics 1988; 79(12):12-49.
2. Osher SJ, Fedkiw RP. Level Set Methods and Dynamic Implicit Surfaces. Springer: New York, 2002.
3. Sethian JA. Level Set Methods and Fast Marching Methods. Cambridge University Press: New York, 1999.
4. Barth TJ, Sethian JA. Numerical schemes for the Hamilton-Jacobi and level set equations on triangulated domains. Journal of Computational Physics 1998; 145(1):1-40.
5. Johnson C. Numerical Solution of Partial Differential Equations by the Finite Element Method. Cambridge University Press: Cambridge, MA, 1987.
6. Hansbo P. Explicit streamline diffusion finite element methods for the compressible Euler equations in conservation variables. Journal of Computational Physics 1993; 109(2):274-288.
7. Mourad HM, Garikipati K. Advances in the numerical treatment of grain boundary migration: coupling with mass transport and mechanics. Journal of Computational Physics, submitted.
8. Ji H, Mourad HM, Fried E, Dolbow JE. Kinetics of thermally-induced swelling of hydrogels. International Journal of Solids and Structures 2005, in press.
9. Zhao H-K, Chan T, Merriman B, Osher S. A variational level set approach to multiphase motion. Journal of Computational Physics 1996; 127(1):179-195.
10. Malladi R, Sethian JA, Vemuri BC. Shape modeling with front propagation: a level set approach. IEEE Transactions on Pattern Analysis and Machine Intelligence 1995; 17(2):158-175.
11. Garikipati K, Rao V. Recent advances in models for thermal oxidation of silicon. Journal of Computational Physics 2001; 174(1):138-170.
12. Sussman M, Fatemi E. An efficient, interface preserving level set redistancing algorithm and its application to interfacial incompressible fluid flow. SIAM Journal on Scientific Computing 1999; 20(4):1165-1191.
13. Dolbow JE, Fried E, Ji H. A numerical strategy for investigating the kinetic response of stimulus responsive hydrogels. Computer Methods in Applied Mechanics and Engineering 2005, in press.
14. Chessa J, Belytschko T. An enriched finite element method and level sets for axisymmetric two-phase flow with surface tension. International Journal for Numerical Methods in Engineering 2003; 58(13):2041-2064.
15. Peng D, Merriman B, Osher S, Zhao H, Kang M. A PDE-based fast local level set method. Journal of Computational Physics 1999; 155(2):410-438.
16. Sethian JA, Vladimirsky A. Ordered upwind methods for static Hamilton-Jacobi equations: theory and algorithms. SIAM Journal on Numerical Analysis 2003; 41(1):325-363.
17. Sethian JA, Adalsteinsson D. An overview of level set methods for etching, deposition, and lithography development. IEEE Transactions on Semiconductor Manufacturing 1997; 10(1):167-184.
18. Sethian JA. An analysis of flame propagation. Ph.D. Dissertation, University of California, Berkeley, 1982.
19. Zhang Y-T, Shu C-W. High-order WENO schemes for Hamilton-Jacobi equations on triangular meshes. SIAM Journal on Scientific Computing 2003; 24(3):1005-1030.
20. Brooks AN, Hughes TJR. Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering 1982; 32:199-259.
21. Chopp DL. Computing minimal surfaces via level set curvature flow. Journal of Computational Physics 1993; 106(1):77-91.