An hp-adaptive finite element/boundary element coupling method for electromagnetic problems

Computational Mechanics

Volumn 39, Issue 5, 2007, Pages 673-680

  Stephan, E P ^a   Maischak, M ^a   Leydecker, F ^a  

^a Leibniz Universität Hannover   (Germany)

Author keywords

Adaptive algorithm; Electromagnetic problems; Fem bem coupling; Hp version; Residual error estimator

Indexed keywords

ADAPTIVE ALGORITHMS; ADAPTIVE SYSTEMS; BOUNDARY ELEMENT METHOD; ERROR ANALYSIS; FINITE ELEMENT METHOD; MAXWELL EQUATIONS; POLYNOMIALS; PROBLEM SOLVING;

ELECTROMAGNETIC PROBLEMS; HP-VERSION; RESIDUAL ERROR ESTIMATORS; TANGENTIAL TRACE;

ELECTROMAGNETIC FIELD THEORY;

EID: 33846676673     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-006-0110-5     Document Type: Article

References (20)

1. Bicǎ I (1997) Iterative substructuring algorithms for the p-version Finite Element Method for elliptic problems. PhD thesis, Courant Institute of Mathematical Sciences, New York University
2. Buffa A, Ciarlet P (2001) On traces for functional spaces related to Maxwell's equations. I. An integration by parts formula in Lipschitz polyhedra. Math Methods Appl Sci 24(1): 9-30
3. Demkowicz L, Babuška I (2003) Optimal p interpolation error estimates for edge unite elements of variable order in 2d. SIAM J Numer Anal 41(4): 1195-1208
4. 1, H (curl) and H(div)-conforming projection-based interpolation in three dimensions. Quasi optimal p-interpolation estimates. Comput Methods Appl Mech Eng 194(2-5): 267-296
5. Demkowicz L, Monk P, Vardapetyan L, Rachowicz W (2000) de Rham diagram for hp finite element spaces. Comput Math Appl 39(7-8): 29-38
6. Heuer N (2002) An hp-adaptive refinement strategy for hypersingular operators on surfaces. Numer Methods Partial Differential Eq.18: 396-419
7. Heuer N, Mellado, ME, Stephan EP (2002) Ap-adaptive algorithm for the bem with the hypersingular operator on the plane screen. Int J Numer Methods Eng 53: 85-1.04
8. Heuer N, Leydecker F, Stephan EP (2003) Iterative substructering method for the p-version of the BEM on triangular meshes. Report #60 Inst. Angew. Mathematik, Universität Hannover
9. Hiptmair R (2002) Symmetric coupling for eddy current problems. SIAM J Numer Anal 40: 41-65
10. Hiptmair R (2002) Finite elements in computational electromagnetism. Acta Numer 11: 237-339
11. Leydecker F (2006) hp-version of the boundary element method for electromagnetic problems - error analysis, adaptivity, preconditioners. Dissertation, Hannover University
12. MacCamy, RC, Stephan EP (1983) A boundary element method for an exterior problem for three-dimensional Maxwell's equations. Appl Anal 16(2): 141-163
13. Maischak M (2001) Manual of the software package maiprogs. Report #48 Inst. Angew. Mathematik, Universität Hannover
14. Muñoz-Sola R (1997) Polynomial liftings on a tetrahedron and applications to the h-p version of the finite element method in three dimensions. SIAM J Numer Anal 34(1): 282-314
15. 3. Numer Math 35: 315-341
16. Schöberl J (2001) Commuting quasi-interpolation operators for mixed finite elements. Preprint ISC-01-10-MATH, Texas A&M University
17. Schwab C (1998) p- and hp-finite element methods. Theory and applications in solid and fluid mechanics. In Numerical mathematics and scientific computation. The Clarendon Press, Oxford University Press, New York
18. Stephan EP, Maischak MA (2005) posteriori error estimates for fem-bem couplings of three-dimensional electromagnetic problems. Comput Methods Appl Mech Eng 194(2-5): 441-452
19. Stephan EP, Wendland WL (1976) Remarks to Galerkin and least squares methods with finite elements for general elliptic problems. Manuscripta Geodaetica, 1: 93-123
20. 3. Report #52, Inst. Angew. Mathematik, Universität Hannover