Implicit-explicit residual error estimator for the coupling of dual-mixed finite elements and boundary elements in elastostatics

Mathematical Methods in the Applied Sciences

Volumn 24, Issue 3, 2001, Pages 179-191

  Gatica, Gabriel N ^a   Heuer, Norbert ^a   Stephan, Ernst P ^b  

^a UNIVERSITY OF CONCEPCIÓN   (Chile)

^b LEIBNIZ UNIVERSITY HANNOVER   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY ELEMENT METHOD; ERROR ANALYSIS; FINITE ELEMENT METHOD; PROBLEM SOLVING;

DIRICHLET-NEUMANN PROBLEMS;

ELASTICITY;

EID: 0035251584     PISSN: 01704214     EISSN: None     Source Type: Journal    
DOI: 10.1002/1099-1476(200102)24:3<179::AID-MMA204>3.0.CO;2-M     Document Type: Article

References (28)

1. Costabel M. A symmetric method for the coupling of finite elements and boundary elements. In The Mathematics of Finite Elements and Applications VI, Whiteman JR (ed). Academic Press: London, 1988; 281-288.
2. Costabel M, Stephan EP. Coupling of finite element and boundary element methods for an elasto-plastic interface problem. SIAM Journal on Numerical Analysis 1990; 27:1212-1226.
3. Hsiao GC. The coupling of boundary element and finite element methods. Zeitschrift für Angewandte Mathematik und Mechanik 1990; 70:493-503. A plenary lecture at the GAMM-Tagung 1989.
4. Gatica GN, Wendland WL. Coupling of mixed finite elements and boundary elements for linear and nonlinear elliptic problems. Applicable Analysis 1996; 63:39-75.
5. Brink U, Carstensen C, Stein E. Symmetric coupling of boundary elements and Raviart-Thomas-type mixed finite elements in elastostatics. Numerische Mathematik 1996; 75:153-174.
6. Meddahi S, Valdés J, Menéndez O, Pérez P. On the coupling of boundary integral and mixed finite element methods, Journal of Computational and Applied Mathematics 1996; 69:113-124.
7. Gatica GN. Combination of mixed finite element and Dirichlet-to-Neumann methods in nonlinear plane elasticity. Applied Mathematics Letters 1997; 10:29-35.
8. Bank RE, Weiser A. Some a posteriori error estimators for elliptic partial differential equations. Mathematics of Computation 1985; 44:283-301.
9. Brink U, Stephan EP. Implicit residual error estimators for the coupling of finite elements and boundary elements. Mathematical Methods in the Applied Sciences 1999; 22:923-936.
10. Ainsworth M, Oden JT. A unified approach to a posteriori error estimation using element residual methods. Numerische Mathematik 1993; 65:23-50.
11. Ainsworth M, Oden JT, A posteriori error estimation in finite element analysis. Computer Methods in Applied Mechanics and Engineering 1997; 142:1-88.
12. Verführt R. A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques. Wiley-Teubner: Chichester, 1996.
13. Carstensen C, Stephan EP. Adaptive boundary element methods for some first kind integral equations. SIAM Journal on Numerical Analysis 1996; 33:2166-2183.
14. Mund P, Stephan EP, Tran T. Hierarchical basis preconditioners for first kind integral equations. Applicable Analysis 1997; 65:353-372.
15. Carstensen C, Stephan EP. Adaptive coupling of boundary elements and finite elements. RAIRO Modélisation Mathematique Analyse Numérique 1995; 29:779-817.
16. Carstensen C, Funken SA, Stephan EP. On the adaptive coupling of FEM and BEM in 2-D elasticity. Numerische Mathematik 1997; 77:187-221.
17. Mund P, Stephan EP. An adaptive two-level method for the coupling of nonlinear FEM-BEM equations. SIAM Journal on Numerical Analysis 1999; 36:1001-1021.
18. Gatica GN, Meddahi S. An a-posteriori error estimate for the coupling of BEM and mixed-FEM. Numerical Functional Analysis and Optimization 1999; 20:449-472.
19. Carstensen C, Funken SA. Coupling of mixed finite elements and boundary elements. Technical Report 98-25, Christian-Albrechts-Universität, Mathematisches Seminar, Kiel, Germany, 1998. IMA Journal of Numerical Analysis, 2000; 20:461-480.
20. Gatica GN, Meddahi S. A dual-dual mixed formulation for nonlinear exterior transmission problems. Preprint 99-04, Departamento de Ingeniería Matemática, Universidad de Concepción, Chile, 1999. Mathematics of Computation, Electronically published May 23, 2000.
21. Gatica GN, Heuer N. An expanded mixed finite element approach via a dual-dual formulation and the minimum residual method. Preprint 99-08, Departamento de Ingeniería Matemática, Universidad de Concepción, Chile, 1999. Journal of Computational and Applied Mathematics, to appear.
22. Gatica GN, Heuer N. A dual-dual formulation for the coupling of mixed-FEM and BEM in hyperelasticity. SIAM Journal on Numerical Analysis 2000; 38:380-400.
23. Barrientos MA, Gatica GN, Stephan EP. A mixed finite element method for nonlinear elasticity: two-fold saddle point approach and a-posteriori error estimate. Preprint 99-25, Departamento de Ingeniería Matemática, Universidad de Concepción, Chile, 1999.
24. Hsiao GC, Stephan EP, Wendland WL. On the Dirichlet problem in elasticity for a domain exterior to an arc. Journal of Computational and Applied Mathematics 1991; 34:1-19.
25. Costabel M. Boundary integral operators on Lipschitz domains: elementary results. SIAM Journal on Mathematical Analysis 1988; 19:613-626.
26. Arnold DN, Brezzi F, Douglas JR, J. PEERS: a new mixed finite element for plane elasticity. Japan Journal of Applied Mathematics 1984; 1:347-367.
27. Stenberg R. A family of mixed finite elements for the elasticity problem. Numerische Mathematik 1988; 53:513-538.
28. C. Carstensen, An a posteriori error estimate for a first-kind integral equation. Mathematics of Computation 1997; 66:139-155.