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To solve multiphysics problems, weak coupling of finite element calculations can be carried out: the subproblems of which the physical nature differs are solved separately on their own meshes. In this case, Galerkin projection provides useful tool to ensure the transfer of physical fields between different meshes. In terms of implementation, the Galerkin projection system can be either accurately assembled over the intersection of two meshes or approximately integrated over the target mesh. This paper describes and compares these two implementation techniques for the Galerkin projection. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Coupled problems are made up of subproblems of which the physical nature differs. Using indirect coupling models, the subproblems are calculated separately on their own meshes to ensure precision. To obtain a precise solution for the total problem, it is important to ensure the transmission of information between the subproblems. In this paper, we present field projection methods on overlapping domains. In comparison to earlier works, the classical L^2 or \bf L^2 projection theory is extended to H(\bf grad), \bf H(\bf curl) and \bf H(div) to obtain increased projection accuracy for the distributional derivatives. A Petrov–Galerkin method is then presented to fill the test space using a biorthogonal basis, without losing the optimality of the result in comparison to the L^2 or \bf L^2 Ritz–Galerkin method. Using the Petrov–Galerkin method and biorthogonal test functions, the projection is presented using a diagonal matrix. However, in the standard Ritz–Galerkin projections, a linear system must be solved. [ABSTRACT FROM AUTHOR]