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We propose a stabilized finite element method for the approximation of the biharmonic equation with a clamped boundary condition. The mixed formulation of the biharmonic equation is obtained by introducing the gradient of the solution and a Lagrange multiplier as new unknowns. Working with a pair of bases forming a biorthogonal system, we can easily eliminate the gradient of the solution and the Lagrange...
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 interface 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,...
Mortar techniques provide a flexible tool for the coupling of different discretization schemes or triangulations. Here, we consider interface problems within the framework of mortar finite element methods. We start with a saddle point formulation and show that the interface conditions enter into the right-hand side. Using dual Lagrange multipliers, we can work with scaled sparse matrices, and static...
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