Computational Mechanics

, Volume 59, Issue 6, pp 1003–1030 | Cite as

Three embedded techniques for finite element heat flow problem with embedded discontinuities

  • M. Davari
  • R. Rossi
  • P. Dadvand
Original Paper


The present paper explores the solution of a heat conduction problem considering discontinuities embedded within the mesh and aligned at arbitrary angles with respect to the mesh edges. Three alternative approaches are proposed as solutions to the problem. The difference between these approaches compared to alternatives, such as the eXtended Finite Element Method (X-FEM), is that the current proposal attempts to preserve the global matrix graph in order to improve performance. The first two alternatives comprise an enrichment of the Finite Element (FE) space obtained through the addition of some new local degrees of freedom to allow capturing discontinuities within the element. The new degrees of freedom are statically condensed prior to assembly, so that the graph of the final system is not changed. The third approach is based on the use of modified FE-shape functions that substitute the standard ones on the cut elements. The imposition of both Neumann and Dirichlet boundary conditions is considered at the embedded interface. The results of all the proposed methods are then compared with a reference solution obtained using the standard FE on a mesh containing the actual discontinuity.


Finite element Shape function Discontinuities 



The authors wish to acknowledge the support of the ERC through the uLites (FP7-314891), NUMEXA (FP7-611636) and REALTIME (FP7-246643) projects.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of Civil and Environmental EngineeringPolytechnic University of CataloniaBarcelonaSpain
  2. 2.Department of Civil and Environmental Engineering, International Center for Numerical Methods in Engineering (CIMNE)Polytechnic University of CataloniaBarcelonaSpain

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