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
The purpose of this paper is to study the superconvergence properties of Ritz-Volterra projection.Through construction a new type of Green function and making use of its properties and the principle of duality,the pap...The purpose of this paper is to study the superconvergence properties of Ritz-Volterra projection.Through construction a new type of Green function and making use of its properties and the principle of duality,the paper proves that the Ritz-Volterra projection defined on r-1 order finite element spaces of Lagrange type in one and two space variable cases possesses O(h2r^2)order and O(h4+1|Inh|)order nodal superconvergence,respectively,and the same type of superconver-gence results are demonstrated for the semidiscrete finite dement approximate solutions of Soboleve-quations.展开更多
Using the interpolation postprocessing technique, some asymptotically exact a posteriori error estimates and global superconvergence results are derived for the finite element Ritz-Volterra projection. These results a...Using the interpolation postprocessing technique, some asymptotically exact a posteriori error estimates and global superconvergence results are derived for the finite element Ritz-Volterra projection. These results are also given for the finite element approalmation to Sobolev equations.展开更多
Presents a study that applied a general error analysis framework for the finite volume element (FVE) approximation to the Ritz-Volterra projection, the Sobolev equations and parabolic integro-differential equations. F...Presents a study that applied a general error analysis framework for the finite volume element (FVE) approximation to the Ritz-Volterra projection, the Sobolev equations and parabolic integro-differential equations. Formulation of the FVE methods in linear finite element spaces defined on a triangulation; Information on the L[sub2] and H1 norm error estimates; Approximations to Sobolev equations and parabolic integro-differential equations.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The purpose of this paper is to study the superconvergence properties of Ritz-Volterra projection.Through construction a new type of Green function and making use of its properties and the principle of duality,the paper proves that the Ritz-Volterra projection defined on r-1 order finite element spaces of Lagrange type in one and two space variable cases possesses O(h2r^2)order and O(h4+1|Inh|)order nodal superconvergence,respectively,and the same type of superconver-gence results are demonstrated for the semidiscrete finite dement approximate solutions of Soboleve-quations.
文摘Using the interpolation postprocessing technique, some asymptotically exact a posteriori error estimates and global superconvergence results are derived for the finite element Ritz-Volterra projection. These results are also given for the finite element approalmation to Sobolev equations.
文摘Presents a study that applied a general error analysis framework for the finite volume element (FVE) approximation to the Ritz-Volterra projection, the Sobolev equations and parabolic integro-differential equations. Formulation of the FVE methods in linear finite element spaces defined on a triangulation; Information on the L[sub2] and H1 norm error estimates; Approximations to Sobolev equations and parabolic integro-differential equations.
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.
