Calcolo manuscript No. (will be inserted by the editor) Mortar finite elements for a heat transfer problem on sliding meshes S. Falletta 1,⋆ , B.P. Lamichhane 2 1 Dip. Matematica-Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino (IT), e-mail: falletta@calvino.polito.it 2 Mathematical Sciences Institute, Australian National University ACT0200, Can- berra, e-mail: Bishnu.Lamichhane@maths.anu.edu.au Received: date / Revised version: date Abstract. We consider a heat transfer problem with sliding bodies, where heat is generated on the interface due to friction. Neglecting the mechanical part, we assume that the pressure on the contact in- terface is a known function. Using mortar techniques with Lagrange multipliers, we show existence and uniqueness of the solution in the continuous setting. Moreover, two different mortar formulations are analyzed, and optimal a priori estimates are provided. Numerical re- sults illustrate the flexibility of the approach. Key words. Mortar finite elements, Lagrange multiplier, saddle point problem, domain decomposition, interface problem. Mathematics Subject Classification (1991): 65N30, 65N55 1. Introduction We consider here the problem of two bodies sliding on each other and generating heat due to contact friction (see also [10,13,14,16, 19,23]). We denote by Ω k ⊂ R d , d ∈{2, 3}, the two disjoint regions occupied by the bodies during the sliding process, and by ∂Ω k the The work was supported by the EU-IHP Breaking Complexity project, CEE HPRN-CT-2002-00286. ⋆ Corresponding author: Please send hard copies or offprint requests to Sil- via Falletta, e-mail: falletta@calvino.polito.it. Present address: Dip. Matematica- Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino (Italy)