An Adaptive Least Squares Mixed Finite Element Method For Pseudo-Parabolic Integro-Differential Equations

In this paper, an adaptive, least-squares mixed finite element method is studied for pseudo-parabolic integro-differential equations. Introducing the auxiliary variables, the equation with initial and boundary value is split into lower order system, then an adaptive least squares mixed finite element method is applied for the lower order system, and the optimal estimates are obtained for the unknown function and its flux. In this paper, the solutions of least-squares mixed weak formulation and mixed finite element are proved. A posteriori error estimator is constructed based on the least-squares functional and the posteriori errors are obtained.Moreover,the priori error estimate of the scheme is analyzed.The main results of this paper are outlined as follows:In chapter one. the paper briefly introduces the development process of adaptive least squares mixed finite element method and some basic knowledge used in this paper.In chapter two, the paper studies the adaptive least squares mixed finite element method for pseudo-parabolic integro-differential equations.