Dorr M, On the discretization of inter-domain coupling in elliptic boundary value problems. In Second International Symposium on Domain Decomposition Methods for Partial Di#erential Equations, Chan T, Glowinski R, Periaux J, Widlund O. (eds). SIAM, Philadelphia, PA 1989; 17--37.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... For the mortar #nite element approximation, this connection comes from de#ning the Lagrange multiplier space using the mesh on one of the subdomains [3] For the LBB condition, one is often required to use a multiplier space on a mesh which is somewhat coarser than the mesh on the subdomains [1, 5, 6, 8]. We consider an approximation technique proposed in Reference [9] which utilizes a #nite element discretization on one subdomain and a mixed #nite element discretization on the other. Such a situation may arise when one wants to couple two existing implementations for numerical simulation of ....

Dorr M, On the discretization of inter-domain coupling in elliptic boundary value problems. In Second International Symposium on Domain Decomposition Methods for Partial Di#erential Equations, Chan T, Glowinski R, Periaux J, Widlund O. (eds). SIAM, Philadelphia, PA 1989; 17--37.

....method provides an approach to glue together the approximations on the subdomains by imposing, in a weak sense, the continuity of the solution across these interfaces. Since the introduction of the mortar method as a coupling technique for spectral and finite element approximations (see, e.g. [8, 9, 10, 22]) it has become a very successful technique Date: August 28, 2000. 1991 Mathematics Subject Classification. 65F10, 65N30. Key words and phrases. mortar, finite element method, Lagrange multipliers, domain decomposition. This work was supported by the National Science Foundation under grant DMS ....

M. Dorr, On the discretization of inter-domain coupling in elliptic boundary-value problems via the p-version of the finite element method, in Domain Decomposition Methods, T. F. Chan, R. Glowinski, J. Periaux, and O. B. Widlund, eds., SIAM, 1989. pp. 17--37.

....subdomains. To get accurate approximation with such meshes, various techniques have been developed. Since meshes do not align, the resulting spaces are necessarily nonconforming. Approximate continuity conditions are imposed by the use of a Lagrange multiplier [1] 2] 4] 5] 6] 7] 12] [14], 15] 16] 21] There are two approaches for Date: July 24, 1998 beginning; Today is August 18, 1999. 1991 Mathematics Subject Classification. 65F10, 65N20, 65N30. Key words and phrases. combined mixed and standard Galerkin discretization methods, non matching grids, preconditioning. This ....

.... approximation, this connection comes from defining the Lagrange multiplier space from the mesh on one of the subdomains [6] For the LBB condition, one often is required to use a multiplier space with a mesh size which is somewhat coarser than the mesh sizes on the subdomains [1] 3] 9] [14]. We consider an approximation technique proposed in [23] which utilizes a finite element discretization on one subdomain and a mixed finite element discretization on the other. This pair of approximations gives rise to a natural variational reformulation of the original problem into a saddle ....

M. Dorr, On the discretization of inter-domain coupling in elliptic boundary value problems, in 2'nd Int. Symp. Domain Dec. Meth. Partial Di#. Eqs., (T. Chan, R. Glowinski, J. Periaux, and O. Widlund, eds), SIAM, Phil. (1989), pp. 17--37.

....biorthogonal wavelets, stabilization, preconditioning. AMS subject classification: 65N55. 1 Introduction In this paper we deal with domain decomposition of elliptic problems by the Three Fields Formulation, developed in [BM93, BM94] Differently from other non conforming formulations [BMP94, Dor89] of domain decomposition, weak continuity is not imposed by requiring that the jump across the interface is orthogonal to a suitable multiplier space, but by introducing the space Phi of traces of functions in H 1( Omega Gamma on the interface Sigma. The This work has been supported partly ....

M. R. Dorr. On the discretization of interdomain coupling in elliptic boundaryvalue problems. In T. Chan, R. Glowinski, J. Periaux, and O. Widlund, editors, Second Internat. Symp. on Domain Decomposition Methods for Partial Differential Equations. SIAM, 1989.

....subdomains. To get accurate approximation with such meshes, various techniques have been developed. Since meshes do not align, the resulting spaces are necessarily nonconforming. Approximate continuity conditions are imposed by the use of a Lagrange multiplier [1] 2] 4] 5] 6] 7] 12] [14], 15] 16] 21] There are two approaches for the analysis. The first treats the method as a nonconforming finite element approximation where the Lagrange multiplier constraints serve to define the nonconforming approximation subspace. The second approach is based on an appropriate ....

.... approximation, this connection comes from defining the Lagrange multiplier space from the mesh on one of the subdomains [6] For the LBB condition, one often is required to use a multiplier space with a mesh size which is somewhat coarser than the mesh sizes on the subdomains [1] 3] 9] [14]. We consider an approximation technique proposed in [23] which utilizes a finite element discretization on one subdomain and a mixed finite element discretization on the other. This pair of approximations gives rise to a natural variational reformulation of the original problem into a saddle ....

M. Dorr, On the discretization of inter-domain coupling in elliptic boundary value problems, in 2'nd Int. Symp. Domain Dec. Meth. Partial Diff. Eqs., (T. Chan, R. Glowinski, J. Periaux, and O. Widlund, eds), SIAM, Phil. (1989), pp. 17--37.

....study how 8 MARY F. WHEELER AND IVAN YOTOV 40 36 32 27 23 19 14 10 Figure 2. Oil concentration contours at 281 days. reduction of mortar degrees of freedom affects the number of interface iterations and the flux discretization error on the interface. Similar ideas have been explored by Dorr in [15]. We solve a single phase flow problem on a 32 Theta 32 Theta 32 domain with a highly correlated log normal permeability field and one injection and three production wells at the corners. A 2 Theta 2 Theta 2 domain decomposition is employed. This example suites well the purpose of our study, ....

M. R. Dorr, On the discretization of interdomain coupling in elliptic boundary value problems, Second International Symposiumon Domain DecompositionMethods (T. F. Chan et al., eds.), SIAM, Philadelphia, 1989, pp. 17--37.

....call this a two field method, the two fields being the interior solution variable and a Lagrange multiplier corresponding to the interface space. Other examples of two field non conforming methods (some defined only at the inter element, rather than the inter sub domain level) may be found e.g. in [18, 14, 23]. There are also three field methods in the literature, where an additional space, corresponding to the trace of the true solution u, is defined on the interface. This forms the third field. Now the jumps u i Gammau and u j Gammau are respectively made orthogonal to two separate Lagrange ....

M. Dorr. On the discretization of inter-domain coupling in elliptic boundary-value problems via the p version of the finite element method in Domain Decomposition methods (T. F. Chan, R. Glowinski, J. Periaux, O. B. Widlund, editors). SIAM, 1989.

....ij = e ij . Then, the supremum (2.11) is taken over functions with zero at endpoints of the edges, which makes it possible to prove a poly logarithmic bound. For another approach, imposing zeros at crosspoint directly, see [41] 2.4. 5 Lagrange Multipliers and Poincar e Steklov Operators Following [19], we show how Lagrange multiplier approach to enforcing solution continuity is related to interface formulations using Poincar eSteklov operators defined in Section 2.4.1. The discrete multi domain case will be treated in the next chapter. We consider the problem from Section 2.4.1 and the ....

....equality 2 X i=1 a k (u k ; v k ) Gamma Z Gamma ( v 1 Gamma v 2 ) u 1 Gamma u 2 )d Gamma = 2 X i=1 Z Omega i fv k ; for all (v 1 ; v 2 ; 2 H 1 D( Omega 1 ) Theta H 1 D( Omega 2 ) Theta (H 1=2 00 ( Gamma) 0 . This problem has a unique solution [19] which is the solution of the problem (Q 1 Q 2 ) R 2 f 2 Gamma R 1 f 1 This is the equation (2.6) It shows that solving the Lagrange multiplier formulation is equivalent to finding Neumann interface data on Gamma (cf. 18] The paper [19] uses the Lagrange formulation to introduce ....

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M. R. Dorr. On the discretization of interdomain coupling in elliptic boundary--value problems. In T. F. Chan, R. Glowinski, J. P'eriaux, and O. B. Widlund, editors, Domain Decomposition Methods, pages 17--37. SIAM, Philadelphia, 1989.

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M. R. Dorr: ÒOn the discretization of interdomain coupling in elliptic boundary value problems,Ó Second International Symposium on Domain Decomposition Methods, T.F. Chan et al., eds., SIAM, Philadelphia, 17-37, 1989.

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