Finite Element Method Of Several Types Of Non-local Initial Boundary Value Problems

Firstly, the paper gives simple introduction about current development of non-local problem. Secondly, we mainly study four kinds of boundary conditions of Poisson equation including Bitsadze-Samarskii problem and its general situation, integral boundary conditions and its homogeneous form. The finite element numerical solution method is applied to solve the four kinds of boundary conditions of Poisson equation in detail.In front of the three types, we build a bilinear space H1(Ω), its finite element subspace Vh and interpolation function uiI. We introduces H*1(Ω), which is linear subspaces of H1(Ω), finite element subspace V*h and interpolation function uI* in the last case. The paper uses bilinear finite element method to solve the above problems as well as analysis and proves the convergence of fi-nite element strictly. In addition, several numerical tests are finished to demonstrate corresponding result coincide with theoretical analysis.