图象恢复中的超收敛

Super Convergence in Picture Restoration

图象恢复中象与原象的关系可以表示为一个非线性积分一微分方程。本文证明了在一致三角剖分的条件下，该方程有限元解的超逼近性质。最后利用有限元的后处理技术证明了该数值解的整体超收敛性。

The relation of image and image points in picture restoration problem can be expressed as nonlinear integral differential equation. How to deal with this kind of equation is a very important problem in applied mathematics. In this paper, we use FEM to solve this equation and successive process technique to deal with the FEM solution Theoretic at analysis has been made to show that the solution has super convergence and whole super convergence property if the FEM space is uniform triangular mesh.