对流扩散方程双线性有限元解的一致估计

A Uniform Error Estimate for Bilinear Finite Element Solution of Advection-diffusion Equations

证明了对流扩散方程的半离散双线性Galerkin有限元方法关于小参数ε一致的最优阶误差估计,其中的常数只与初值和右端函数有关,而与小参数ε无关.

In this paper we prove an optimal-order error estimate for semidiscrete bilinear Calerkin finite element method for time-dependent advectiomdiffusion equations, in which the general constants depend only on the Sobolev norms of the initial and right data, but not on the scaling parameter ε.