Uniform $L^1$ error bounds for semi-discrete finite element solutions of evolutionary integral equations

Lin, Qun, Xu, Da, and Zhang, Shuhua. "Uniform $L^1$ error bounds for semi-discrete finite element solutions of evolutionary integral equations." Applications of Mathematics 2012. Prague: Institute of Mathematics AS CR, 2012. 144-162. <http://eudml.org/doc/287834>.

@inProceedings{Lin2012,
abstract = {In this paper, we consider the second-order continuous time Galerkin approximation of the solution to the initial problem $u_\{t\}+\int _\{0\}^\{t\}\beta (t-s) Au(s)ds=0,u(0)=v,t>0,$ where A is an elliptic partial-differential operator and $\beta (t)$ is positive, nonincreasing and log-convex on $(0,\infty )$ with $0\le \beta (\infty )<\beta (0^\{+\})\le \infty $. Error estimates are derived in the norm of $L^\{1\}_\{t\}(0,\infty ;L^\{2\}_\{x\})$, and some estimates for the first order time derivatives of the errors are also given.},
author = {Lin, Qun, Xu, Da, Zhang, Shuhua},
booktitle = {Applications of Mathematics 2012},
keywords = {evolutionary integral equation; semi-discrete finite element solution; uniform error bound; Galerkin approximation; elliptic partial-differential operator},
location = {Prague},
pages = {144-162},
publisher = {Institute of Mathematics AS CR},
title = {Uniform $L^1$ error bounds for semi-discrete finite element solutions of evolutionary integral equations},
url = {http://eudml.org/doc/287834},
year = {2012},
}

TY - CLSWK
AU - Lin, Qun
AU - Xu, Da
AU - Zhang, Shuhua
TI - Uniform $L^1$ error bounds for semi-discrete finite element solutions of evolutionary integral equations
T2 - Applications of Mathematics 2012
PY - 2012
CY - Prague
PB - Institute of Mathematics AS CR
SP - 144
EP - 162
AB - In this paper, we consider the second-order continuous time Galerkin approximation of the solution to the initial problem $u_{t}+\int _{0}^{t}\beta (t-s) Au(s)ds=0,u(0)=v,t>0,$ where A is an elliptic partial-differential operator and $\beta (t)$ is positive, nonincreasing and log-convex on $(0,\infty )$ with $0\le \beta (\infty )<\beta (0^{+})\le \infty $. Error estimates are derived in the norm of $L^{1}_{t}(0,\infty ;L^{2}_{x})$, and some estimates for the first order time derivatives of the errors are also given.
KW - evolutionary integral equation; semi-discrete finite element solution; uniform error bound; Galerkin approximation; elliptic partial-differential operator
UR - http://eudml.org/doc/287834
ER -