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Heterogeneous coupling by virtual control methods. (English) Zbl 1002.65133

The authors propose the application of the virtual control method for advection-diffusion problems. Although this technique has been introduced before in the domain decomposition method with overlapping subdomains for homogeneous problems, in this work virtual control is used to treat heterogeneous problems. In fact, virtual control is used to achieve interface continuity for both cases of overlapping or non overlapping subdomains.
The method is convergent since it is shown that the cost functionals tend to zero when the viscosity coefficient tends to zero. In addition, to assess the theoretical analysis, the authors present the results of the numerical experiments for different 1D and 2D problems.

MSC:

65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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