Error Estimation Of Finite Volume Element Method Based On Crouzeix-Raviart Element

The finite volume element method is simple in structure and can keep the local conservation of numerical flow.It is widely used in the computational fluid dynamics and electromagnetic fields.This thesis is divided into two parts.In the first part,we study the approximation error of the upwind finite volume element method based on Crouzeix-Raviart nonconforming finite element method for convection diffusion problems in the 1-norm posteriori error estimation.The main goal is from the the upwind scheme based on the conforming finite element and the scheme without upwind based on CrouzeixRaviart nonconforming finite volume element.Using the upwind scheme to treat the convection term,we get the global upper bound of a posteriori error estimator in the1-norm.In the second part,we study the a priori estimates of the approximation error of the finite volume element method with Crouzeix-Raviartfor element for the nonlinear elliptic problem,as well as the a posteriori error estimation in the 1-and 2-norm are derived.