R. A. Adams and J. F. Fournier, Sobolev spaces, Pure and Applied Mathematics, vol.140, 2003.

G. Akrivis and C. Makridakis, Galerkin time-stepping methods for nonlinear parabolic equations, ESAIM: Mathematical Modelling and Numerical Analysis, vol.38, issue.2, pp.261-289, 2004.
DOI : 10.1051/m2an:2004013
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.96.1923

I. Babu?ka and M. Suri, The $h-p$ version of the finite element method with quasiuniform meshes, ESAIM: Mathematical Modelling and Numerical Analysis, vol.21, issue.2, pp.199-238, 1987.
DOI : 10.1051/m2an/1987210201991

I. Babu?ka and M. Suri, -Version of the Finite Element Method, SIAM Journal on Numerical Analysis, vol.24, issue.4, pp.750-776, 1987.
DOI : 10.1137/0724049

G. Barles and P. Souganidis, Convergence of approximation schemes for fully nonlinear second order equations, 29th IEEE Conference on Decision and Control, pp.271-283, 1991.
DOI : 10.1109/CDC.1990.204046

J. F. Bonnans and H. Zidani, Consistency of Generalized Finite Difference Schemes for the Stochastic HJB Equation, SIAM Journal on Numerical Analysis, vol.41, issue.3, pp.1008-1021, 2003.
DOI : 10.1137/S0036142901387336
URL : https://hal.archives-ouvertes.fr/inria-00072460

S. C. Brenner and L. R. Scott, The mathematical theory of finite element methods, Texts in Applied Mathematics, vol.15, 2008.

F. Camilli and M. Falcone, An approximation scheme for the optimal control of diffusion processes, ESAIM: Mathematical Modelling and Numerical Analysis, vol.29, issue.1, pp.97-122, 1995.
DOI : 10.1051/m2an/1995290100971

H. O. Cordes, ???ber die erste Randwertaufgabe bei quasilinearen Differentialgleichungen zweiter Ordnung in mehr als zwei Variablen, Mathematische Annalen, vol.38, issue.3, pp.278-312, 1956.
DOI : 10.1007/BF01342965

M. G. Crandall and P. L. Lions, Convergent difference schemes for nonlinear parabolic equations and mean curvature motion, Numerische Mathematik, vol.75, issue.1, pp.17-41, 1996.
DOI : 10.1007/s002110050228

K. Debrabant and E. R. Jakobsen, Semi-Lagrangian schemes for linear and fully non-linear diffusion equations, Mathematics of Computation, vol.82, issue.283, pp.1433-1462, 2013.
DOI : 10.1090/S0025-5718-2012-02632-9
URL : http://arxiv.org/abs/0910.1046

D. Pietro, D. A. Ern, and A. , Mathematical aspects of discontinuous Galerkin methods, Mathématiques & Applications, vol.69, 2012.
DOI : 10.1007/978-3-642-22980-0

W. H. Fleming and H. M. Soner, Controlled Markov processes and viscosity solutions, Stochastic Modelling and Applied Probability, 2006.

D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order, Classics in Mathematics, 2001.

P. Grisvard, Elliptic problems in nonsmooth domains, Classics in Applied Mathematics SIAM, vol.69, 2011.
DOI : 10.1137/1.9781611972030

M. Jensen and I. Smears, On the Convergence of Finite Element Methods for Hamilton--Jacobi--Bellman Equations, SIAM Journal on Numerical Analysis, vol.51, issue.1, pp.137-162, 2013.
DOI : 10.1137/110856198

H. J. Kushner, Numerical Methods for Stochastic Control Problems in Continuous Time, SIAM Journal on Control and Optimization, vol.28, issue.5, pp.999-1048, 1990.
DOI : 10.1137/0328056

A. Maugeri, D. K. Palagachev, and L. G. Softova, Elliptic and parabolic equations with discontinuous coefficients, Mathematical Research, vol.109, 2000.
DOI : 10.1002/3527600868

P. Monk and E. Süli, The Adaptive Computation of Far-Field Patterns by A Posteriori Error Estimation of Linear Functionals, SIAM Journal on Numerical Analysis, vol.36, issue.1, pp.251-274, 1999.
DOI : 10.1137/S0036142997315172

I. Mozolevski, E. Süli, and P. R. Bösing, hp-Version a priori Error Analysis of Interior Penalty Discontinuous Galerkin Finite Element Approximations to the Biharmonic Equation, Journal of Scientific Computing, vol.39, issue.3, pp.465-491, 2007.
DOI : 10.1007/s10915-006-9100-1

M. Renardy and R. C. Rogers, An introduction to partial differential equations, Texts in Applied Mathematics, vol.13, 2004.

D. Schötzau and C. Schwab, Time Discretization of Parabolic Problems by the HP-Version of the Discontinuous Galerkin Finite Element Method, SIAM Journal on Numerical Analysis, vol.38, issue.3, pp.837-875, 2000.
DOI : 10.1137/S0036142999352394

I. Smears and E. Süli, Discontinuous Galerkin Finite Element Approximation of Nondivergence Form Elliptic Equations with Cord??s Coefficients, SIAM Journal on Numerical Analysis, vol.51, issue.4, pp.2088-2106, 2013.
DOI : 10.1137/120899613

I. Smears and E. Süli, Discontinuous Galerkin Finite Element Approximation of Hamilton--Jacobi--Bellman Equations with Cordes Coefficients, SIAM Journal on Numerical Analysis, vol.52, issue.2, pp.993-1016, 2014.
DOI : 10.1137/130909536

V. Thomée, Galerkin finite element methods for parabolic problems, 2006.
DOI : 10.1007/978-3-662-03359-3

J. Wloka, Partial differential equations, 1987.
DOI : 10.1017/CBO9781139171755