A priori error estimation provides information about the asymptotic behavior of the approximate solution and information on convergence rates of the problem. Contrarily, a posteriori error estimation derives the estimation of the exact error by employing the approximate solution and provides a practical accurate error estimation. Additionally, a posteriori error estimates can be used to steer adaptive schemes, that is to decide the refinement processes, namely local mesh refinement or local order refinement schemes. Adaptive schemes of finite element methods for numerical solutions of partial differential equations are considered standard tools in science and engineering to achieve better accuracy with minimum degrees of freedom. In this thesis, we focus on a posteriori error estimations of mixed finite element methods for nonlinear time dependent partial differential equations. Mixed finite element methods are methods which are based on mixed formulations of the problem. In a mixed fo.....

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Error estimations of H1 mixed finite element method for the Benjamin-Bona-Mahony equation are considered. The problem is reformulated into a system of first order partial differential equations, which allows an approximation of the unknown function and its derivative. Local parabolic error estimates are introduced to approximate the true errors from the computed solutions; the so-called a posteriori error estimates. Numerical experiments show that the a posteriori error estimates converge to the true errors of the problem...

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