Volumetric coupling approaches for multiphysics simulations on non-matching meshes

P. Farah, A. T. Vuong, W. A. Wall, A. Popp

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


In finite element analysis of volume coupled multiphysics, different meshes for the involved physical fields are often highly desirable in terms of solution accuracy and computational costs. We present a general methodology for volumetric coupling of different meshes within a monolithic solution scheme. A straightforward collocation approach is compared to a mortar-based method for nodal information transfer. For the latter, dual shape functions based on the biorthogonality concept are used to build the projection matrices, thus further reducing the evaluation costs. We give a detailed explanation of the integration scheme and the construction of dual shape functions for general first-order and second-order Langrangian finite elements within the mortar method, as well as an analysis of the conservation properties of the projection operators. Moreover, possible incompatibilities due to different geometric approximations of curved boundaries are discussed. Numerical examples demonstrate the flexibility of the presented mortar approach for arbitrary finite element combinations in two and three dimensions and its applicability to different multiphysics coupling scenarios.

Original languageEnglish
Pages (from-to)1550-1576
Number of pages27
JournalInternational Journal for Numerical Methods in Engineering
Issue number12
StatePublished - 21 Dec 2016


  • collocation
  • dual mortar method
  • monolithic solution scheme
  • nodal information transfer
  • non-matching meshes
  • volume coupling


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