Brenner, Susanne C.; Sung, Li-yeng; Gedicke, Joscha \(P_1\) finite element methods for an elliptic optimal control problem with pointwise state constraints. (English) Zbl 1464.65061 IMA J. Numer. Anal. 40, No. 1, 1-28 (2020). Summary: We present theoretical and numerical results for two \(P_1\) finite element methods for an elliptic distributed optimal control problem on general polygonal/polyhedral domains with pointwise state constraints. Cited in 9 Documents MSC: 65K10 Numerical optimization and variational techniques 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 49M41 PDE constrained optimization (numerical aspects) Keywords:elliptic distributed optimal control problems; pointwise state constraints; nonconvex domains; variational inequalities; \(P_1\) finite element; mass lumping PDFBibTeX XMLCite \textit{S. C. Brenner} et al., IMA J. Numer. Anal. 40, No. 1, 1--28 (2020; Zbl 1464.65061) Full Text: DOI