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- W4386841283 abstract "In this paper we present and analyze a weighted residual a posteriori error estimate for an optimal control problem. The problem involves a nondifferentiable cost functional, a state equation with an integral fractional Laplacian, and control constraints. We employ subdifferentiation in the context of nondifferentiable convex analysis to obtain first-order optimality conditions. Piecewise linear polynomials are utilized to approximate the solutions of the state and adjoint equations. The control variable is discretized using the variational discretization method. Upper and lower bounds for the a posteriori error estimate of the finite element approximation of the optimal control problem are derived. In the region where 3/2 < alpha < 2, the residuals do not satisfy the L2(Omega) regularity. To address this issue, an additional weight is included in the weighted residual estimator, which is based on a power of the distance from the mesh skeleton. Furthermore, we propose an h-adaptive algorithm driven by the posterior view error estimator, utilizing the Dorfler labeling criterion. The convergence analysis results show that the approximation sequence generated by the adaptive algorithm converges at the optimal algebraic rate. Finally, numerical experiments are conducted to validate the theoretical results." @default.
- W4386841283 created "2023-09-19" @default.
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- W4386841283 date "2023-09-14" @default.
- W4386841283 modified "2023-09-27" @default.
- W4386841283 title "Adaptive finite element approximation of sparse optimal control with integral fractional Laplacian" @default.
- W4386841283 doi "https://doi.org/10.48550/arxiv.2309.08130" @default.
- W4386841283 hasPublicationYear "2023" @default.
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