Solving Second-order Elliptic Problem In Domain With Curved Boundaries By Quadrilateral Finite Element On Adaptive Grids

We solve second-order elliptic problem in domains with curved boundaries.In order to acquire the proper convergence order,the adaptive grids of quadrilateral finite element are used.The error estimations with H~1-norm are obtained inΩ_h~l.Through using the skills of parameters equations,the error estimations also are obtained inΩ\Ω_h~l.Therefore, the whole error estimations are obtained in the curved domainΩ.It has the same convergence order as convex polygon with the precise quadrilateral mesh.The paper introduces the practice of multi-level adaptive method.And it also has some advantages in solving the finite element problem of curved domains.And give some definitions and methods related to this paper.Numerical example is given to demonstrate validity of our theoretical analysis.