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In this paper we conduct a priori and a posteriori error analysis of the$C^0$ interior penalty method for Hamilton-Jacobi-Bellman equations, withcoefficients that satisfy the Cordes condition. These estimates show thequasi-optimality of the method, and provide one with an adaptive finite elementmethod. In accordance with the proven regularity theory, we only assume thatthe solution of the Hamilton-Jacobi-Bellman equation belongs to $H^2$.

Adaptive $C^0$ interior penalty methods for Hamilton-Jacobi-Bellman equations with Cordes coefficients