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 relat...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.展开更多
This paper studies the finite element method for some nonlinear hyperbolic partial differential equations with memory and dampling terms.A Crank\|Nicolson approximation for this kind of equations is presented.By using...This paper studies the finite element method for some nonlinear hyperbolic partial differential equations with memory and dampling terms.A Crank\|Nicolson approximation for this kind of equations is presented.By using the elliptic Ritz\|Volterra projection,the analysis of the error estimates for the finite element numerical solutions and the optimal H \+1\|norm error estimate are demonstrated.展开更多
基金Supported by Postdoctoral Fundation of China and by Doctoral Start Fundation of Liaoning Province
文摘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.
文摘This paper studies the finite element method for some nonlinear hyperbolic partial differential equations with memory and dampling terms.A Crank\|Nicolson approximation for this kind of equations is presented.By using the elliptic Ritz\|Volterra projection,the analysis of the error estimates for the finite element numerical solutions and the optimal H \+1\|norm error estimate are demonstrated.
