Arbitrary-level hanging nodes and automatic adaptivity in the hp-FEM

Mathematics and Computers in Simulation

Volumn 77, Issue 1, 2008, Pages 117-132

  Šolín, Pavel ^a,b   Červený, Jakub ^a,b   Doležel, Ivo ^b  

^a UNIVERSITY OF TEXAS AT EL PASO   (United States)

^b INSTITUTE OF THERMOMECHANICS   (Czech Republic)

Author keywords

35B50; 65N60; Automatic hp adaptivity; Constrained approximation; Hanging nodes; hp FEM

Indexed keywords

ELASTICITY; FINITE ELEMENT METHOD; PROBLEM SOLVING;

AUTOMATIC HP-ADAPTIVITY; CONSTRAINED APPROXIMATION; HANGING NODES;

ADAPTIVE ALGORITHMS;

EID: 38749111846     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matcom.2007.02.011     Document Type: Article

References (29)

1. Aksoylu B., Bond S., and Holst M. An Odyssey into local refinement and multilevel preconditioning III: implementation and numerical experiments. SIAM J. Sci. Comput. 25 (2003) 478-498
2. Babuška I., Griebel M., and Pitkaranta J. The problem of selecting the shape functions for p-type elements. Int. J. Num. Methods Eng. 28 (1989) 1891-1908
3. Babuška I., and Gui W. The h, p and hp-versions of the finite element method in 1 dimension-Part I. The error analysis of the p-version. Numer. Math. 49 (1986) 577-612
4. Babuška I., and Gui W. The h, p and hp-versions of the finite element method in 1 dimension-Part II. The error analysis of the h and hp-versions. Numer. Math. 49 (1986) 613-657
5. Babuška I., and Gui W. The h, p and hp-versions of the finite element method in 1 dimension-Part III. The adaptive hp-version. Numer. Math. 49 (1986) 659-683
6. Babuška I., and Guo B.Q. Approximation properties of the hp version of the finite element method. Comput. Methods Appl. Mech. Eng. 133 (1996) 319-346
7. Babuška I., Szabo B., and Katz I.N. The p-version of the finite element method. SIAM J. Numer. Anal. 18 (1981) 515-545
8. Babuska I., Izadpanah K., and Szabo B. The postprocessing technique in the finite element method. The theory and experience. In: Kardestuncer H. (Ed). Unification of Finite Element Methods (1984), Elsevier Science Publishers B.V., North-Holland 97-121
9. Bauer A.C., and Patra A.K. Performance of parallel preconditioners for adaptive hp-FEM discretizations of incompressible flows. Commun. Numer. Methods Eng. 18 (2002) 305-313
10. Bauer A.C., and Patra A.K. Robust and efficient domain decomposition preconditioners for adaptive hp finite element approximation for linear elasticity with and without discontinuous coefficients. Int. J. Numer. Methods Eng. 59 (2004) 337-364
11. Bertolazzi E. Discrete conservation and discrete maximum principle for elliptic PDEs. Math. Models Methods Appl. Sci. 8 (1998) 685-711
12. Demkowicz L., Oden J.T., Rachowicz W., and Hardy O. Toward a universal hp-adaptive finite element strategy. Part 1: constrained approximation and data structure. Comput. Methods Appl. Math. Eng. 77 (1989) 79-112
13. L. Demkowicz, W. Rachowicz, P. Devloo, A fully automatic hp-adaptivity. TICAM Report No. 01-28, University of Texas at Austin, 2001.
14. Karniadakis G.E., and Sherwin S.J. Spectral/hp Element Methods for CFD (1999), Oxford University Press, Oxford
15. Laszloffy A., Long J., and Patra A.K. Simple data management, scheduling and solution strategies for managing the irregularities in parallel adaptive hp finite element simulations. Parallel Comput. 26 (2000) 1765-1788
16. Melenk J.M. hp-Finite Element Methods for Singular Perturbations (2002), Springer-Verlag, Berlin (Lecture Notes in Mathematics 1796)
17. Pardo D., and Demkowicz L. Integration of hp-adaptivity and a two grid solver for elliptic problems. Comput. Methods Appl. Mech. Eng. 195 7/8 (2006)
18. M. Paszynski, J. Kurtz, L. Demkowicz, Parallel, fully automatic hp-adaptive 2D finite element package, TICAM Report 04-07, The University of Texas at Austin, 2004.
19. Peano A.G. Hierarchies of conforming finite elements for plane elasticity and plate bending. Comput. Math. Appl. 2 (1976) 211-224
20. Rachowicz W., and Demkowicz L. An hp-adaptive finite element method for electromagnetics. Part II: A 3D implementation. Int. J. Numer. Methods Eng. 53 (2002) 147-180
21. Schwab C. p- and hp-Finite Element Methods, Theory and Applications to Solid and Fluid Mechanics (1998), Oxford University Press, New York
22. Šolín P. Partial Differential Equations and the Finite Element Method (2005), J. Wiley & Sons
23. Šolín P., and Demkowicz L. Goal-oriented hp-adaptivity for elliptic problems. Comput. Methods Appl. Mech. Eng. 193 (2004) 449-468
24. Šolín P., Segeth K., and Doležel I. Higher-Order Finite Element Methods (2003), Chapman & Hall/CRC Press, Boca Raton
25. Šolín P., and Vejchodský T. On a weak discrete maximum principle for hp-FEM. J. Comput. Appl. Math. 209 (2007) 54-65
26. Zítka M., Šolín P., Vejchodský T., and Avila F. Imposing orthogonality to hierarchic higher-order finite elements. Math. Comput. Simul. 76 (2007) 211-217
27. Szabo B., and Babuška I. Finite Element Analysis (1991), J. Wiley & Sons, New York p. 368
28. T. Vejchodský, P. Šolín, Discrete maximum principle for higher-order finite elements in 1D, Math. Comput., November 2006, in press.
29. Vejchodský T., Šolín P., and Zítka M. Modular hp-FEM system HERMES and its application to the Maxwell's equations. Math. Comput. Simul. 76 (2007) 223-228