Optimal control of elliptic surface PDEs with pointwise bounds on the\n state

2016/06/09 by Ahmad Ahmad Ali, Ali, Ahmad Ahmad, Michael Hinze +3
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Contact Mechanics and Variational Inequalities

paper · pdf · doi:10.48550/arxiv.1606.03025

Abstract

We consider a linear-quadratic optimization problem with pointwise bounds on\nthe state for which the constraint is given by the Laplace-Beltrami equation\n(to have uniqueness we add an lower order term) on a two-dimensional surface .\nBy using finite elements we approximate the optimization problem by a family of\ndiscrete problems and prove convergence rates for the discrete controls and the\ndiscrete states. Furthermore, assuming (roughly spoken) a higher regularity for\nthe control the order of convergence improves. This extends a result known in\nan Euclidean setting to the surface case.\n

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