The Finite Element Method And A Posteriori Error Analysis Of Nonlocal Diffusion Problems With Volume Constraints

In this thesis, we consider homogeneous and inhomogeneous nonlocal diffusion prob-lems with volume constraints. We only study the finite element method of inhomogeneous nonlocal diffusion problems with volume constraints in one and two dimension in this the-sis. In order to the expression of code in the numerical calculation, the coding principle of elements and nodes is given as well. In addition, we propose a new and effective numerical method for the homogeneous nonlocal diffusion problem with volume constraints and its error analysis comes subsequently. A posteriori error estimator is consequently prompted for the nonlocal diffusion problem with volume constraints, the reliability and efficiency of the estimator are proved. After a series of analytical arguments, the convergence of the nonlocal a posteriori error estimator to its local counterpart is proved when the horizon parameter δ→0. We give some experiments to verify the theoretical conclusions.