Hierarchic finite element bases on unstructured tetrahedral meshes

International Journal for Numerical Methods in Engineering

Volumn 58, Issue 14, 2003, Pages 2103-2130

  Ainsworth, Mark ^a   Coyle, Joe ^a  

^a UNIVERSITY OF STRATHCLYDE   (United Kingdom)

Author keywords

Conforming finite element spaces; Hierarchic finite element bases

Indexed keywords

APPROXIMATION THEORY; FINITE ELEMENT METHOD; POLYNOMIALS;

TETRAHEDRAL ELEMENTS;

HIERARCHICAL SYSTEMS;

FINITE ELEMENT ANALYSIS;

EID: 0348044407     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.847     Document Type: Article

References (36)

1. Bossavit A. Computational Electromagnetism: Variational Formulation, Complementarity, Edge Elements. Academic Press: New York, 1998.
2. Brezzi F, Fortin M. Mixed and Hybrid Finite Element Methods. Springer-Verlag: Berlin, 1991.
3. Jin J. The Finite Element Method in Electromagnetics. Wiley: New York, 1993.
4. Silvester P, Ferrari R. Finite Elements for Electrical Engineers. Cambridge University Press: Cambridge, 1996.
5. Schwab C. p- and hp-finite element methods: theory and applications in solid and fluid mechanics. Numerical Mathematics and Scientific Computation. Oxford University Press: Oxford, 1998.
6. Szabo B, Babuska I. Finite Element Analysis. Wiley: New York, 1991.
7. Karniadakis G, Sherwin S. Spectral/hp Element Methods for CFD. Oxford University Press: Oxford, 1999.
8. 3. Numerische Mathematik 1980; 93:315-341.
9. 3. Numerische Mathematik 1986; 50:57-81.
10. Hiptmair R. Canonical construction of finite elements. Mathematics of Computing 1999; 68(228):1325-1346.
11. Bossavit A. A rationale for edge-elements in 3-d fields computations. IEEE Transactions on Magnetics 1988; 24(1):74-79.
12. Mur G. Edge elements, their advantages and their disadvantages. IEEE Transactions on Magnetics 1994; 30(5):3552-3557.
13. Webb JP. Edge elements and what they can do for you. IEEE Transactions on Antennas and Propagation 1993; 29:1460-1465.
14. Whitney H. Geometric Integration Theory. Princeton University Press: Princeton, 1957.
15. Cendes Z. Vector finite elements for electromagnetic field computation. IEEE Transactions on Magnetics 1991; 27(5):3958-3967.
16. Geuzaine C, Meys B, Dular P, Legros W. Convergence of high order curl-conforming finite elements. IEEE Transactions on Magnetics 1999; 35(3):1442-1444.
17. Kameari A. Calculation of transient 3D eddy current using edge-elements. IEEE Transactions on Magnetics 1990; 26:466-469.
18. Lee J-F, Sun D-K, Cendes Z. Full-wave analysis of dielectric waveguides using tangential vector finite elements. IEEE Transactions on Microwave Theory and Techniques 1991; 39(8):1262-1271.
19. Bossavit A, Mayergoyz I. Edge elements in scattering problems. IEEE Transactions on Magnetics 1989; 25(4):2816-2821.
20. Kameari A. Symmetric second order edge elements for triangles and tetrahedra. IEEE Transactions on Magnetics 1999; 35(3):1394-1397.
21. Lee J-F, Sun D-K, Cendes Z. Tangential vector finite elements for electromagnetic field computation. IEEE Transactions on Magnetics 1991; 27(5):4032-4035.
22. Mur G, de Hoop A. A finite element method for three-dimensional electromagnetic fields in inhomogeneous media. IEEE Transactions on Magnetics 1985; 21(6):2188-2191.
23. Webb JP, Forghani B. Hierarchical scalar and vector tetrahedra. IEEE Transactions on Magnetics 1993; 29(2):1495-1498.
24. Andersen L, Volakis J. Hierarchical tangential vector finite elements for tetrahedra. IEEE Microwave and Guided Wave Letters 1998; 8(3):127-129.
25. Graglia RD, Wilton DR, Peterson AF. Higher order interpolatory vector bases for computational electromagnetics. IEEE Transactions on Antennas and Propagation 1997; 45(3):329-342.
26. Webb JP. Hierarchical vector basis functions of arbitrary order for triangular and tetrahedral finite elements. IEEE Transactions on Antennas and Propagation 1999; 47(8):1244-1253.
27. Demkowicz L, Vardapetyan L. Modeling of electromagnetic absorption/scattering problems using hp-adaptive finite elements. Computer Methods in Applied Mechanics and Engineering 1998; 152(1-2):103-124.
28. Demkowicz L, Monk P, Vardapetyan L, Rachowicz W. De Rham diagram for hp finite element spaces. Technical Report, TICAM Report 99-6, University of Texas at Austin, 1999.
29. Ainsworth M, Coyle J. Hierarchic hp-edge element families for Maxwell's equations on hybrid quadrilateral/triangular meshes. Computer Methods in Applied Mechanics and Engineering 2001; 190:6709-6733.
30. Ciarlet PG. The Finite Element Method for Elliptic Problems. Elsevier, North-Holland: Amsterdam, 1978.
31. Akin JE. Finite Elements in Analysis and Design. Academic Press: New York, 1994.
32. Ainsworth M, Senior B. hp-Finite element procedures on non-uniform geometric meshes: adaptivity and constrained approximation. In Grid Generation and Adaptive Algorithms, Bern MW, Flaherty JE, Luskin M (eds), vol. 113. IMA: Minnesota, 1999; 1-29.
33. Gradshteyn IS, Ryzhik IM. In Table of Integrals, Series and Products (5th edn), Jeffrey A (ed.). Academic Press Ltd.: UK, 1994.
34. Marsden JE, Hughes TJR. Mathematical Foundations of Elasticity. Prentice-Hall: Englewood Cliffs, NJ, 1983.
35. Ainsworth M, Senior B. Aspects of an adaptive hp-finite element method: adaptive strategy, conforming approximation and efficient solvers. Computer Methods in Applied Mechanics and Engineering 1997; 150:65-87.
36. Kron G. A set of principles to interconnect the solutions of physical systems. Journal of Applied Physics 1953; 24(8):965-980.