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In the first part of the paper, we study the discontinuous Galerkin (DG) and$C^0$ interior penalty ($C^0$-IP) finite element approximation of the periodicstrong solution to the fully nonlinear second-orderHamilton--Jacobi--Bellman--Isaacs (HJBI) equation with coefficients satisfyingthe Cordes condition. We prove well-posedness and perform abstract a posterioriand a priori analyses which apply to a wide family of numerical schemes. Theseperiodic problems arise as the corrector problems in the homogenization of HJBIequations. The second part of the paper focuses on the numerical approximationto the effective Hamiltonian of ergodic HJBI operators via DG/$C^0$-IP finiteelement approximations to approximate corrector problems. Finally, we providenumerical experiments demonstrating the performance of the numerical schemes.

esaim. mathematical modelling and numerical analysis

Discontinuous Galerkin and $C^0$-IP finite element approximation of  periodic Hamilton--Jacobi--Bellman--Isaacs problems with application to  numerical homogenization