摘要
The purpose of this paper is to study the stability and approximation properties of Ritz-Volterra projection. Through constructing a new type of Green functions and making use of various properties and estimates related with the functions, we prove that the Ritz-Volterra projection defined on the finite-dimensional subspace S_h of H_o^1 possesses the W_p^1-stability and the optimal approxi mation properties in W_p^1 and L_p for 2≤p≤∞. Our results, in this paper, can be applied to the finite element approximations for many evolution equations such as parabolic and hyperbolic integrodifferential equations,Sobolevequations and visco-elasticity, etc.
The purpose of this paper is to study the stability and approximation properties of Ritz-Volterra projection. Through constructing a new type of Green functions and making use of various properties and estimates related with the functions, we prove that the Ritz-Volterra projection defined on the finite-dimensional subspace S_λ of H^1_0 possesses the W^1_p-stability and the optimal approximation properties in W^1_p and Lp for 2≤p≤∞. Our results, in this paper, can be applied to the finite element approximations for many evolution equations such as parabolic and hyperbolic integro-differential equations, Sobolev equations and visco-elasticity, etc.
基金
Supported by Postdoctoral Fundation of China and by Doctoral Start Fundation of Liaoning Province
