拟线性拋物方程半离散变网格有限元方法的误差估计  

ERROR ESTIMATES FOR CONTINUOUS-TIME GALERKIN MESH MODIFICATION FOR QUASI-LINEAR PARA BOLIC EQUATIONS

作　　者：孙澈[1] 

机构地区：[1]南开大学数学系

出　　处：《计算数学》1990年第4期440-448,共9页Mathematica Numerica Sinica

基　　金：国家自然科学基金

摘　　要：§1.导言近年来,变网格方法正日益为人们所重视与应用,但理论性分析文献仍不多见。文献[1]讨论了某些发展型方程变网格方法的误差估计,但未给出收敛阶估计;文献[2,3]仅对全离散方法讨论了收敛阶问题。本文对一类拟线性抛物问题,于第二节中给出了半离散Galerkin变网格计算格式及其可解性定理;第三节中建立了对称误差估计;In this paper, Galerkin mesh modification for parabolic problems are studied. The sym-metric error estimates are derived for n-dimensional quasi-linear initial-boundary value pro-blems. An optimal convergence order estimate with the norm associated with a symmetric estimate is established under appropriate assumptions. The L^2 estimate for the changing mesh Galerkin procedure for the one-dimensional semilinear parabolic problem is also discussed and an optimal order convergence estimate is obtained.

关 键 词：有限元法 变网格 误差估计 

分 类 号：O242.21[理学—计算数学]