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- W1923442614 abstract "We study a discretization technique for a linear-quadratic optimal control problem involving fractional diffusion of order $s in (0,1)$. Since fractional diffusion can be realized as the Dirichlet-to-Neumann map for a nonuniformly elliptic equation, we recast our problem as a nonuniformly elliptic optimal control problem. The rapid decay of the solution suggests a truncation that is suitable for numerical approximation. We discretize the truncated problem with a fully discrete scheme based on a piecewise linear finite element approximation on quasi-uniform meshes for the optimal control. The state variable is approximated via first--degree tensor product finite elements on anisotropic meshes. Based on derived Holder and Sobolev regularity results for the optimal control, we develop an a priori error analysis for $s in (0,1)$. Numerical experiments validate the derived error estimates." @default.
- W1923442614 created "2016-06-24" @default.
- W1923442614 creator A5044773525 @default.
- W1923442614 date "2015-08-12" @default.
- W1923442614 modified "2023-09-27" @default.
- W1923442614 title "A first-degree FEM for an optimal control problem of fractional operators: error analysis" @default.
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