A finite element method for surface PDEs: Matrix properties

Numerische Mathematik

Volumn 114, Issue 3, 2009, Pages 491-520

  Olshanskii, Maxim A ^a   Reusken, Arnold ^b  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

^b RWTH AACHEN UNIVERSITY   (Germany)

Author keywords

58J32; 65N15; 65N30; 76D45; 76T99

Indexed keywords

EID: 72749084586     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00211-009-0260-4     Document Type: Article

References (9)

1. Braess D.: Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics, 3rd edn. Cambridge University Press, London (2007).
2. Deckelnick, K., Dziuk, G., Elliott, C. M., Heine, C.-J.: An h-narrow band finite element method for elliptic equations on implicit surfaces. IMA J. Numer. Anal., doi:10.1093/imanum/drn049 (2009).
3. Demlow A., Dziuk G.: An adaptive finite element method for the Laplace-Beltrami operator on implicitly defined surfaces. SIAM J. Numer. Anal. 45, 421-442 (2007).
4. DROPS package. http://www.igpm.rwth-aachen. de/DROPS/.
5. Dziuk G.: Finite elements for the beltrami operator on arbitrary surfaces. In: Hildebrandt, S., Leis, R. (eds) Partial Differential Equations and Calculus of Variations. Lecture Notes in Mathematics, vol. 1357, pp. 142-155. Springer, Heidelberg (1988).
6. James A., Lowengrub J.: A surfactant-conserving volume-of-fluid method for interfacial flows with insoluble surfactant. J. Comp. Phys. 201, 685-722 (2004).
7. Muradoglu M., Tryggvason G.: A front-tracking method for computation of interfacial flows with soluble surfactant. J. Comput. Phys. 227, 2238-2262 (2008).
8. Olshanskii, M. A., Reusken, A.: A finite element method for surface PDEs: Matrix properties, Preprint 287, IGPM, RWTH Aachen, earlier version of this paper (2008).
9. Olshanskii, M. A., Reusken, A., Grande, J.: An eulerian finite element method for elliptic equations on moving surfaces. Accepted to SIAM J. Numer. Anal. (2009).