Optimal control and numerical adaptivity for advection-diffusion equations
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An adaptive algorithm is proposed for solving the Stokes problem with continuous, piecewise linear stabilized finite elements and meshes with high aspect ratio. Anisotropic, a posteriori error estimates in the H-1 x L-2 norm are derived, the constant being ...
A one-dimensional free surface problem is considered. It consists in Burgers' equation with an additional diffusion term on a moving interval. The well-posedness of the problem is investigated and existence and uniqueness results are obtained locally in ti ...
Some new domain decomposition methods (DDM) based on optimal control approach are introduced for the coupling of first- and second-order equations on overlapping subdomains. Several cost functionals and control functions are proposed. Uniqueness and existe ...
Some new domain decomposition methods (DDM) based on optimal control approach are introduced for the coupling of first- and second-order equations on overlapping subdomains. Several cost functionals and control functions are proposed. Uniqueness and existe ...
We investigate in this paper a numerical method to control the temperature of an induction heating process through electric current parameters such as frequency and current voltage imposed to the terminals of the inductor. We seek a sinusoidal voltage func ...
In this paper we recall a stabilization technique for finite element methods for convection-diffusion-reaction equations, originally proposed by Douglas and Dupont. The method uses least square stabilization of the gradient jumps a across element boundarie ...
We consider a heterogeneous model for the dynamics of a blood solute both in the vascular lumen and inside the arterial wall. In the lumen, we consider an advection-diffusion equation, where the convective field is provided by the velocity of blood, which ...
We present an extension of a 2D cartesian electromagnetic and thermal model to achieve the optimal control of an industrial induction heating system. The control variables are the frequency and the power. We explain how to derive the discrete optimal contr ...
Current and future directions in the development of numerical methods and numerical software for control problems are discussed. Major challenges include the demand for higher accuracy, robustness of the method with respect to uncertainties in the data or ...
The anisotropic error indicator presented in [M. Picasso, Comm. Numer. Methods Engrg., 19 (2003), pp. 13-23.] in the frame of the Laplace equation is extended to elliptic and parabolic problems. Our error indicator is derived using the anisotropic interpol ...