# Adaptive discontinuous galerkin methods for non-linear reactive flows

The aim of this thesis is to solve the convection/reaction dominated non-stationary semi-linear diffusion-convection-reaction problems with internal/boundary layers in an accurate and efficient way using a time-space adaptive algorithm. We use for space discretization the symmetric interior penalty discontinuous Galerkin method, and backward Euler for time discretization. Our main interest is to derive robust residual-based a posteriori error estimators both in space and time. To derive the a posteriori bounds for the fully discrete system, we utilize the elliptic reconstruction technique. The use of elliptic reconstruction technique allows us to use the a posteriori error estimators derived for stationary models and to obtain optimal orders in $L^{\infty}(L^2)$ norms.