Design and application of a gradient-weighted moving finite element code II: In two dimensions

SIAM Journal on Scientific Computing

Volumn 19, Issue 3, 1998, Pages 766-798

  Carlson, Neil N ^a   Miller, Keith ^b  

^a PURDUE UNIVERSITY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Adaptive grids; Deforming grids; Drift diffusion equations; Finite elements; Motion by mean curvature; Moving finite elements; Moving nodes; Nonlinear diffusion; Partial differential equations

Indexed keywords

EID: 0001070724     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827594269561     Document Type: Article

References (19)

1. N. N. CARLSON AND K. MILLER, Design and application of a gradient-weighted moving finite element code I: in 1D, SIAM J. Sci. Comput., 19 (1998), pp. 728-765.
2. K. MILLER, Recent results on finite element methods with moving nodes, in Accuracy Estimates and Adaptive Refinement in Finite Element Calculations, I. Babuška, O. C. Zienkiewicz, J. Gago, and E. R. de A. Oliveira, eds., Wiley, New York, 1986, pp. 325-338.
3. N. N. CARLSON AND K. MILLER, Gradient weighted moving finite elements in two dimensions, in Finite Elements Theory and Application, D. L. Dwoyer, M. Y. Hussaini, and R. G. Voight, eds., Springer Verlag, New York, 1988, pp. 151-164.
4. K. MILLER, A geometrical-mechanical interpretation of gradient-weighted moving finite elements, SIAM J. Numer. Anal., 34 (1997), pp. 67-90.
5. A. KUPRAT, Creation and Annihilation of Nodes for the Moving Finite Element Method, Ph.D. thesis, Department of Mathematics, University of California, Berkeley, CA, 1992.
6. L. HÖRMANDER, Linear Partial Differential Operators, Springer-Verlag, New York, 1969.
7. K. MILLER, Alternate modes to control the nodes in the moving finite element method, in Adaptive Computational Methods for Partial Differential Equations, SIAM, Philadelphia, PA, 1983, pp. 165-182.
8. N. N. CARLSON AND K. MILLER, Design and application of a gradient-weighted moving finite code, Part II, in 2-D, Technical Report 237, Center for Applied Mathematics, Purdue University, West Lafayette, IN, 1994 (this report is an earlier unabridged version of the present paper).
9. T. J. R. HUGHES, The Finite Element Method, Prentice-Hall, Englewood Cliffs, NJ, 1987.
10. C. P. PLEASE AND P. K. SWEBY, A Transformation to Assist Numerical Solution of Diffusion Equations, Numer. Anal. Report 5/86, Department of Mathematics, University of Reading, UK, 1986.
11. P. A. MARKOWICH, Semiconductor Equations, Springer-Verlag, New York, 1990.
12. D. W. PEACEMAN, Fundamentals of Numerical Resevoir Simulation, Elsevier North-Holland, Amsterdam, 1977.
13. K. A. BRAKKE, The Motion of a Surface by Its Mean Curvature, Princeton University Press, Princeton, NJ, 1978.
14. S. OSHER AND J. A. SETHIAN, Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulation, J. Comput. Phys., 79 (1988), pp. 12-49.
15. L. C. EVANS AND J. SPRUCK, Motion of level sets by mean curvature, I, J. Differential Geometry, 33 (1991), pp. 635-681.
16. S. NAZARI, Rotational Surfaces in Euclidean and Hyperbolic Spaces, Mean Curvature Motion, and the Moving Finite Element Method, Ph.D. thesis, Department of Mathematics, University of California, Berkeley, CA, 1993.
17. P. MARCELLINI AND K. MILLER, Regularization for the equation of prescribed mean curvature and for motion by mean curvature, in Curvature Flows and Related Topics, in Proceedings of the Conference at Levico, Italy, 1994, A. Damlamian, ed., Gakkotosho, Tokyo, 1995.
18. G. DZIUK, An algorithm for evolutionary surfaces, Numer. Math., 58 (1991), pp. 603-611.
19. P. A. ZEGELING, Moving-Grid Methods for Time-Dependent Partial Differential Equations, Ph.D. thesis, University of Amsterdam and Centre for Mathematics and Computer Science (CWI), Amsterdam, 1992.