A posteriori error bounds by "local corrections" using the dual mesh

IEEE Transactions on Magnetics

Volumn 35, Issue 3 PART 1, 1999, Pages 1350-1353

  Bossavit, Alain ^a  

^a EDF R AND D   (France)

Author keywords

Complementarity; Dual mesh; Error bounds

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; ERRORS; FINITE ELEMENT METHOD; GALERKIN METHODS; SET THEORY; TENSORS;

COMPLEMENTARITY; DUAL MESH; ERROR BOUNDS;

MAGNETIC FIELDS;

EID: 0033121797     PISSN: 00189464     EISSN: None     Source Type: Journal    
DOI: 10.1109/20.767212     Document Type: Article

References (13)

1. G. Allen, "Variational Inequalities, Complementary Problems and Duality Theory", J. Math. Anal. Appl., 58 (1979), pp. 1-10.
2. A.M. Arthurs, Complementary variational principles, Clarendon Press (Oxford), 1970.
3. A. Bossavit, "Complementarity in Non-Linear Magnetostatics: Bilateral Bounds on the Flux-Current Characteristic", COMPEL, 11, 1 (1992), pp. 9-12.
4. A. Bossavit, Computational Electromagnetism, Academic Press (Boston), 1998.
5. P. Hammond, J. Penman, "Calculation of inductance and capacitance by means of dual energy principles", Proc. IEE, 123, 6 (1976), pp. 554-59.
6. P. Ladévèze, D. Leguillon, "Error estimate procedure in the finite element method and applications", SIAM J. Numer. Anal., 20, 3 (1983), pp. 485-509.
7. B. Noble, "Complementary variational principles for boundary value problems", MRC Technical Report 473, Nov. 1964.
8. W. Prager, J.L. Synge, "Approximations in elasticity based on the concept of function space", Quart. Appl. Math., 5, 3 (1947), pp. 241-69.
9. J.N. Reddy, J.T. Oden, "Convergence of Mixed Finite-Element Approximations of a Class of Linear Boundary-Value Problems", J. Struct. Mech., 2 (1973), pp. 83-108.
10. J.-F. Remade, P. Dular, A. Genon, W. Legros, "A posteriori error estimation and adaptive meshing using error in constitutive relation", IEEE Trans., MAG-32, 3 (1996), pp. 1369-72.
11. J. Rikabi, C.F. Bryant, E.M. Freeman, "Complementary solutions of linear and non-linear magnetostatic problems", IEE Proc., 135-A, 7 (1988), pp. 433-47.
12. J.L. Synge, The Hypercircle in Mathematical Physics, Cambridge U.P. (Cambridge), 1957.
13. K. Washizu, "Bounds for solutions of boundary value problems in elasticity", J. Math. Phys., 32 (1953), pp. 117-28.