| Title:
|
Uniform $L^1$ error bounds for semi-discrete finite element solutions of evolutionary integral equations (English) |
| Author:
|
Lin, Qun |
| Author:
|
Xu, Da |
| Author:
|
Zhang, Shuhua |
| Language:
|
English |
| Journal:
|
Applications of Mathematics 2012 |
| Volume:
|
Proceedings. Prague, May 2-5, 2012 |
| Issue:
|
2012 |
| Year:
|
|
| Pages:
|
144-162 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $0\leq\beta(\infty)<\beta(0^{+})\leq\infty$. 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. (English) |
| Keyword:
|
evolutionary integral equation |
| Keyword:
|
semi-discrete finite element solution |
| Keyword:
|
uniform error bound |
| Keyword:
|
Galerkin approximation |
| Keyword:
|
elliptic partial-differential operator |
| MSC:
|
45D05 |
| MSC:
|
65K05 |
| MSC:
|
65R20 |
| idZBL:
|
Zbl 1313.65336 |
| idMR:
|
MR3204408 |
| . |
| Date available:
|
2017-02-14T09:01:06Z |
| Last updated:
|
2017-04-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/702901 |
| . |
