Direkt zum Inhalt | Direkt zur Navigation

Projekt Anisotrope finite Elemente

Anisotrope finite Elemente

(DFG-Förderung im Rahmen des SFB 393 bis Dezember 2004, Projekte AP 72/3
Förderungszeitraum: bis Dezember 2006)

BEARBEITER UND KOOPERATIONSPARTNER:

INHALT:

  • Anisotrope lokale Interpolationsfehlerabschätzungen
  • Optimale Netzverfeinerungsstrategien für Randwertprobleme mit anisotropen Lösungen
  • anisotrope Fehlerschätzer und adaptive Verfahren für anisotrope Finite-Elemente-Netze
  • inf-sup stabile Finite-Elemente-Paare

VERÖFFENTLICHUNGEN:

Bücher und Dissertationen

  1. Thomas Apel: Anisotropic finite elements: Local estimates and applications. Series "Advances in Numerical Mathematics", Teubner, Stuttgart, 1999. ISBN 3-519-02744-5. Vergriffen! (Habilitationsschrift. Preprint SFB393/99-03, TU Chemnitz, 1999.) [download]
  2. Thomas Apel: Finite-Elemente-Methoden über lokal verfeinerten Netzen für elliptische Probleme in Gebieten mit Kanten. PhD thesis, TU Chemnitz, 1991
  3. Sergey Grosman: Adaptivity in anisotropic finite element calculations. PhD thesis, TU Chemnitz, 2006 [download]

Studienarbeiten

  1. Jens Seidel: Eine Auflösungsmethode für das Finite-Elemente-Gleichungssystem bei anisotroper Diskretisierung in der Umgebung einer Kante, Diplomarbeit, TU Chemnitz, 2002
  2. Sergey Grosman: Robust local problem error estimation for a singularly perturbed reaction-diffusion problem on anisotropic finite element meshes, Master thesis, TU Chemnitz, 2001 [download]
  3. Maharavo Randrianarivony: Stability of mixed finite element methods with anisotropic meshes, Master thesis, TU Chemnitz, 2001

Artikel in referierten Zeitschriften

  1. Sergey Grosman: An equilibrated residual method with a computable error approximation for a singularly perturbed reaction-diffusion problem on anisotropic finite element meshes. Math. Model. Numer. Anal. 40(2006), 239--267
  2. Thomas Apel, Serge Nicaise: The inf-sup condition for the Bernardi-Fortin-Raugel element on anisotropic meshes. Calcolo 41(2004), 89-113 [description | ps-file | pdf-file]
  3. Thomas Apel, Sergei Grosman, Peter K. Jimack, Arnd Meyer: A new methodology for anisotropic mesh refinement based upon error gradients. Appl. Numer. Math. 50(2004), 329-341. [description | preprint: ps.gz pdf]
  4. Thomas Apel, Joachim Schöberl: Multigrid methods for anisotropic edge refinement. SIAM J. Numer. Anal. 40(2002) 5, 1993-2006. [preprint]
  5. Thomas Apel, H. Maharavo Randrianarivony: Stability of discretizations of the Stokes problem on anisotropic meshes. Mathematics and Computers in Simulation 61(2003) 3-6, 437-447. [ description | preprint: ps.gz pdf]
  6. Thomas Apel, Serge Nicaise, Joachim Schöberl: A non-conforming finite element method with anisotropic mesh grading for the Stokes problem in domains with edges. IMA J. Num. Anal. 21(2001)4, 843-856. [description | preprint | published version ]
  7. Thomas Apel, Serge Nicaise, Joachim Schöberl: Crouzeix-Raviart type finite elements on anisotropic meshes. Numer. Math. 89 (2001), 193-223 [preprint | published version]
  8. Thomas Apel, Serge Nicaise: The finite element method with anisotropic mesh grading for elliptic problems in domains with corners and edges. Math. Methods Appl. Sci. 21(1998), 519-549. [ preprint]
  9. Thomas Apel: Interpolation of non-smooth functions on anisotropic finite element meshes. Math. Modeling Numer. Anal. 33(1999) 6, 1149-1185 [ preprint]
  10. Thomas Apel, Gert Lube: Anisotropic mesh refinement for a singularly perturbed reaction diffusion model problem. Appl. Numer. Math. 26(1998), 415-433 [ early preprint]
  11. Thomas Apel: Anisotropic interpolation error estimates for isoparametric quadrilateral finite elements. Computing 60(1998), 157-174 [ preprint]
  12. Thomas Apel, Gert Lube: Anisotropic mesh refinement in stabilized Galerkin methods. Numer. Math. 74(1996), 261-282 [ preprint.]
  13. Thomas Apel, Frank Milde: Comparison of various mesh refinement strategies near edges. Comm. Numer. Methods Engrg. 12(1996), 373-381 [ preprint]
  14. Thomas Apel, Manfred Dobrowolski: Anisotropic interpolation with applications to the finite element method. Computing 47(1992), 277-293
  15. Sergey Grosman: An equilibrated residual method with a computable error approximation for a singularly perturbed reaction-diffusion problem on anisotropic finite element meshes. M2AN, Vol. 40, No. 2, 239-267 (2006).

Eingereichte Arbeiten

  1. Thomas Apel, Tobias Knopp, Gert Lube: Stabilized finite element methods with anisotropic mesh refinement for the Oseen problem.NAM-Preprint 2006.07 Georg-August-Universität Göttingen, 2006. Submitted to Appl. Numer. Math. [preprint]
  2. Thomas Apel, Gunar Matthies: Non-conforming, anisotropic, rectangular finite elements of arbitrary order for the Stokes problem.Bericht 374, Fakultät für Mathematik, Ruhr-Universität Bochum, 2006. [ preprint ]
  3. Sergey Grosman The robustness of the hierarchical a posteriori error estimator for reaction-diffusion equation on anisotropic meshes. Preprint SFB393/04-02, TU Chemnitz, 2004. [preprint]

Tagungsberichte

  1. Gert Lube, Thomas Apel, Tobias Knopp: Stabilized finite element methods with anisotropic mesh refinement for the Oseen problem. In: Proceedings of the Int. Conference on Boundary and Interior Layers, BAIL 2006 [pdf-file]
  2. Thomas Apel, Serge Nicaise, Joachim Schöberl: Finite element methods with anisotropic meshes near edges. In M. Krizek and P. Neittaanmäki (eds.): Proc. Internat. Conf. Finite Element Methods: Three-dimensional Problems. GAKUTO Internat. Series, Math. Sci. Appl., vol. 15, Gakkotosho, Tokyo, 2001, 1-8. [paper]
  3. Thomas Apel, Martin Berzins, Peter Jimack, Gerd Kunert, Alexander Plaks, Igor Tsukerman, Mark Walkley: Mesh Shape and Anisotropic elements: Theory and Practice. In J. R. Whiteman (ed.): The Mathematics of Finite Elements and Applications X, Elsevier, Amsterdam, 2000, 367-376 [paper]
  4. Thomas Apel: Treatment of boundary layers with anisotropic finite elements. Z. Angew. Math. Mech. 78(1998)S3, S855-S856. [ preprint]
  5. Thomas Apel: Anisotropic mesh refinement for the treatment of boundary layers. In M. Bach, C. Constanda, G. C. Hsiao, A.-M. Sändig, P. Werner (eds.): Analysis, numerics and applications of differential and integral equations, Pitman Research Notes in Mathematics 379, Longman, Harlow, 1998, 12-16 [ preprint]
  6. Thomas Apel, Serge Nicaise: Elliptic problems in domains with edges: anisotropic regularity and anisotropic finite element meshes. In J. Cea, D. Chenais, G. Geymonat, J. L. Lions (eds.): Partial Differential Equations and Functional Analysis (In Memory of Pierre Grisvard) Birkhäuser, Boston, 1996, 18-34
  7. Thomas Apel, Roland Mücke, John R. Whiteman: Incorporation of a-priori mesh grading into a-posteriori adaptive mesh refinement. In A. Casal, L. Gavete, C. Conde, J. Herranz (eds.): III Congreso Matematica Aplicada/XIII C.E.D.Y.A. Madrid, 1993 Madrid, 1995, 79-92

Weitere Forschungsberichte

  1. Thomas Apel, Serge Nicaise: The finite element method with anisotropic mesh grading for the Poisson problem in domains with edges. [ paper]
  2. Thomas Apel, Gert Lube: Local inequalities for anisotropic finite elements and their application to convection-diffusion problems. Preprint SPC94_26, TU Chemnitz-Zwickau, 1994 [ paper]