An Improvement of Fems

In this thesis the aim has been to move towards a more advanced simulation for Convection Diffusion Reaction(CDR)problems when the convection term is dominated which require special stabilization techniques to obtain meaningful numerical results. A number of new finite element techniques which are constructed are effective for governing equation in case of small diffusion term and show that these techniques are stable provided that the space-time grid is appropriately constructed. An improvement of finite element approximations Galerkin-Modified parameters(Modified Parameters-Galerkin), Galerkin-New Schemes(New Schemes-Galerkin) and Galerkin-Modified Parameters-New Schemes(Modified Parameters-New Schemes-Galerkin)which are discussing to solve two dimensional time-dependent CDR equation with dominating convection term in equal space to reduce or completely eliminate numerical oscillations. The main idea of such stabilization techniques prevent numerical oscillations and other instabilities in solving problem with high Peclet number (convection term is dominant)by introducing sophisticated way additional viscosity into the discrete equations.