一维椭圆边值问题的自适应Petrov-Galerkin方法

ADAPTIVE PETROV-GALERKIN FEM FOR ELLIPTIC BOUNDARY PROBLEM IN ONE SPACE VARIABLE

讨论了一维椭圆边值问题的基于最佳检验空间之自适应PetrovGalerkin方法,证明了PetrovGalerkin有限元解的E超收敛性,给出了方法误差的局部后验估计,建立了相应的自适应策略.利用椭圆问题的上述结果,对一维非定常对流占优扩散问题,构造了特征PetrovGalerkin自适应算法.

In this paper,an adaptive Petrov Galerkin F.E.M.with optimal test function space is studied.For this method,the extra super convergence is demonstrated and a local posterior error estimate and an adaptive technique are established.Applying the obtained results above,we present a characteristic Petrov Galerkin adaptive scheme for unsteady convection diffusion problem in one space variable.