A deluxe FETI‐DP algorithm for a hybrid staggered discontinuous Galerkin method for H(curl)‐elliptic problems

SUMMARY Convergence theories and a deluxe dual and primal finite element tearing and interconnecting algorithm are developed for a hybrid staggered DG finite element approximation of H(curl) elliptic problems in two dimensions. In addition to the advantages of staggered DG methods, the basis functions of the new hybrid staggered DG method are all locally supported in the triangular elements, and a Lagrange multiplier approach is applied to enforce the global connections of these basis functions. The interface problem on the Lagrange multipliers is further reduced to the resulting problem on the subdomain interfaces, and a dual and primal finite element tearing and interconnecting algorithm with an enriched weight factor is then applied to the resulting problem. Our algorithm is shown to give a condition number bound ofC.1C log.H=h// 2 , independent of the two parameters, whereH=his the number of triangles across each subdomain. Numerical results are included to confirm our theoretical bounds. Copyright © 2013 John Wiley & Sons, Ltd. Received 12 September 2013; Accepted 11 November 2013 In this paper, a dual and primal finite element tearing and interconnecting (FETI-DP) algorithm is developed for a fast and stable solution of a new hybrid staggered DG (HSDG) method applied to H(curl) problems. Staggered DG (SDG) methods were first introduced in [1–3] for wave propagation problems. The idea was subsequently applied to other problems, such as convection-diffusion equations [4], electromagnetic problems [5–9], Stokes equations [10], and multiscale wave simulations [11, 12]. Similar to [5], the advantages of using SDG for H(curl) problems are the preservation of the structures of the differential operators, the local conservation property, and the optimal convergence. In particular, the discretizations of the two curl operators by the SDG method are adjoint to each other, and the null space of the discrete curl operator is exactly the gradients. Moreover, the divergence condition is automatically satisfied in an appropriate weak sense. Despite the aforementioned advantages, the implementation of SDG methods requires careful numbering of the supports of the basis functions. To allow an easier implementation of the SDG method, the HSDG method is introduced in this paper. One distinctive advantage of the HSDG method is that the basis functions are all locally supported in the triangular elements, hence, the numbering can be easily performed. The fact that the basis functions are totally discontinuous requires some global couplings. In particular, we will use the Lagrange multiplier approach to enforce the global connection of the basis functions. This idea is also related to the hybridized DG methods [13–16]. In fact, it is shown that the SDG method is the limit of a hybridized DG method