Abstract
We study the numerical approximation of distributed nonlinear optimal control problems governed by semilinear elliptic partial differential equations with pointwise constraints on the control. Our main result are error estimates for optimal controls in the maximum norm. Characterization results are stated for optimal and discretized optimal control. Moreover, the uniform convergence of discretized controls to optimal controls is proven under natural assumptions.
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Arada, N., Casas, E. & Tröltzsch, F. Error Estimates for the Numerical Approximation of a Semilinear Elliptic Control Problem. Computational Optimization and Applications 23, 201–229 (2002). https://doi.org/10.1023/A:1020576801966
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DOI: https://doi.org/10.1023/A:1020576801966