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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 L2 or L2 projection theory is extended to H(grad), H(curl) and 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 L2 or L2 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.