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We design and analyze a C0 interior penalty method for the approximation of classical solutions of the Dirichlet boundary value problem of the MongeāAmpĆØre equation on convex polygonal domains. The method is based on an enhanced cubic Lagrange finite element that enables the enforcement of the convexity of the approximate solutions. Numerical results that corroborate the a priori and a posteriori error estimates are presented. It is also observed from numerical experiments that this method can capture certain weak solutions.more » « less
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Abstract We investigate a P 1 P_{1} finite element method for an elliptic distributed optimal control problem with pointwise state constraints and a state equation that includes advective/convective and reactive terms.The convergence of this method can be established for general polygonal/polyhedral domains that are not necessarily convex.The discrete problem is a strictly convex quadratic program with box constraints that can be solved efficiently by a primal-dual active set algorithm.more » « less