Abstract This work is devoted to study a doubly non linear elliptic-parabolic problem with quadraticgradient term by Rothe’s method. We investigate the long time behavior of the solution to thediscrete problem and prove the existence of compact global attractor. Our method relays onsemi-discretization with respect to the time variable.Keywords: Semi-discretization, Euler forward scheme, attractor, parabolic, elliptic, existence, uniqueness,stability.2010 Mathematics Subject Classification: 35K55, 35B45, 35B65. 1 Introduction The aim of this paper is to study a doubly non linear elliptic-parabolic equations by means of timediscretization, based on the Euler forward scheme. We will approximate the parabolic problem bya sequence of elliptic problems. We prove the existence of compact global attractor. We will getour results by a semi discretization process. To this end, we investigate first existence, uniquenessand stability results for the semidiscretized problem.We recall that the Euler forward scheme has been used by several authors while studying timediscretization of nonlinear parabolic problems and we refer for example to the works [1, 2, 3, 4, 5,6, 7, 8, 9, 10, 11] and the references cited therein for some details. This scheme is usually used toprove existence of solutions as well as to compute the numerical approximations.*Corresponding author: J. Igbida, E-mail: jigbida@yahoo.frReceived: 11 December 2013Accepted: 08 February 2014Published: 15 September 2014