B. Beck, R. Hiptmair, R. H. W. Hoppe and B. Wohlmuth, Residual based a posteriori error estimator for eddy current computation, M2AN Math. Model. Numer. Anal. 34 (2000), no. 1, 159-182.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....However, since many interpolation estimates in [8] can not be transferred from H 0(## and standard nodal elements to H 0 (curl; ## and Nedelec s elements, the proof turns out to be more technical. In a private communication Hiptmair suggested a proof of (3. 2) using the operator P h introduced in [3]. The projector P h was defined locally and replaced integration on the edges with integration on the faces. This produces an interpolation which is well defined on vector fields in H . By applying a Bramble Hilbert argument, Lemma 5 of [3] shows that #u Ch u 1 , and C u 1 , for all ....

....a proof of (3.2) using the operator P h introduced in [3] The projector P h was defined locally and replaced integration on the edges with integration on the faces. This produces an interpolation which is well defined on vector fields in H . By applying a Bramble Hilbert argument, Lemma 5 of [3] shows that #u Ch u 1 , and C u 1 , for all u first estimate of (3.2) then follows from the best approximation property of h , and the second follows from Ch 1 #(Q P h )u# C#curl P h u# C u 1 . The finite element approximation to (1.1) is the function u h U ....

R. Beck, R. Hiptmair, R. Hoppe, and B. Wohlmuth. Residual based a-posteriori error estimators for eddy current computation. M AN, 34(1):159--182, 2000.

....defined on more regular sub spaces [5] and the global Fortin operators [3] were known to fulfill the commuting diagram property. These new operators are, beyond possibly many other applications, useful to simplify and generalize existing multigrid theory [9, 1] and a posteriori error estimates [2]. 2. Definitions The domain Omega is assumed to be polyhedral and with Lipschitz boundary. It is covered by a shape regular tetrahedral mesh. We define the set of vertices V = fV i g; the set of edges E = fE ij g; the set of faces F = fF ijk g; the set of tetrahedra T = fT ijkl g: The two ....

R. Beck, R. Hiptmair, R. Hoppe, and B. Wohlmuth. Residual based a posteriori error estimators for eddy current computations. M2AN, 34(1):159--182, 2000.

....many types of problems, in particular second order elliptic problems. Among the most widely used approached are residual based error estimators and hierarchical error estimators. We refer to the monograph by Verfurth [33] and the survey articles by Bornemann et al. 11] and Johnson et al. 25] In [6] a residual based a posteriori error estimator for the very edge element approximation of the eddy current problem is studied. The same was done for high frequency scattering problems, i.e. the full Maxwell s equations, in [30] To the knowledge of the authors, hierarchical error estimator for ....

....Remark. If the finite element solution u h is computed by an iterative scheme, we have to take into account an additional iteration error. Then Galerkin orthogonality is not exactly satisfied and the above equivalences have to be augmented by terms incorporating the iteration error (see [6]) 9 4 Numerical experiments Throughout the numerical experiments we use lowest order edge elements on an unstructured tetrahedral grid. The stiffness matrix and load vector corresponding to (3) are computed using Gaussian quadrature of order 5. Interpolation of boundary values is of the same ....

R. BECK, R. HIPTMAIR, R. HOPPE, AND B. WOHLMUTH, Residual based a-posteriori error estimators for eddy current computation, Tech. Rep. 112, SFB 382, Universitat Tubingen, Tubingen, Germany, March 1999. To appear in M AN.

....many types of problems, in particular second order elliptic problems. Among the most widely used approached are residual based error estimators and hierarchical error estimators. We refer to the monograph by Verfurth [33] and the survey articles by Bornemann et al. 11] and Johnson et al. 25] In [6] a residual based a posteriori error estimator for the very edge element approximation of the eddy current problem is studied. The same was done for high frequency scattering problems, i.e. the full Maxwell s equations, in [30] To the knowledge of the authors, hierarchical error estimator for ....

....Remark. If the finite element solution u h is computed by an iterative scheme, we have to take into account an additional iteration error. Then Galerkin orthogonality is not exactly satisfied and the above equivalences have to be augmented by terms incorporating the iteration error (see [6]) 9 4 Numerical experiments Throughout the numerical experiments we use lowest order edge elements on an unstructured tetrahedral grid. The stiffness matrix and load vector corresponding to (3) are computed using Gaussian quadrature of order 5. Interpolation of boundary values is of the same ....

R. BECK, R. HIPTMAIR, R. HOPPE, AND B. WOHLMUTH, Residual based a-posteriori error estimators for eddy current computation, Tech. Rep. 112, SFB 382, Universitat Tubingen, Tubingen, Germany, March 1999. To appear in M 2 AN.

No context found.

B. Beck, R. Hiptmair, R. H. W. Hoppe and B. Wohlmuth, Residual based a posteriori error estimator for eddy current computation, M2AN Math. Model. Numer. Anal. 34 (2000), no. 1, 159-182.

No context found.

R. Beck, R. Hiptmair, R. H. W. Hoppe, and B. Wohlmuth. Residual based a posteriori error estimators for eddy current computation. M2AN Math. Model. Numer. Anal., 34(1):159--182, 2000.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC