【摘要】 <正> §1.引言设H是可分的Hilbert空间,内积为（·,·）,范数为||·||.v是H的稠密子空间.于V定义另一内积[·,·]和相应的范数|·|,使v关于[·,·]具有Hilbert空间结构。假定v往H的嵌入:v|→H连续,即存在常数a>0,使 ||u||≤a|u|,uv. （1） 设L₁,L₂是由v到H的线性算子,其定义域D_L1,D_L2是v的线性稠密子集,且D_L1D_L2.令A=L₁+L₂(显然A的定义域D_A=D_LI)。对H,我们考虑算子方程更多还原

【Abstract】 Consider the linear operator equation Au=L₁u+L₂u=f, where the operator L₁ is V-elliptic（cf.[3]） and L₁^-1L₂ is Compact in the Hilbert space V. A V-estimation of the Convergence rate for the Galerkin method is derived in the first part of this paper. This result includes the well-known theorem due to Mikhlin（[1; §16]）. In the second part the error estimation in H-norm（i.e. L²-norm） under some conditions is investigated.更多还原