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

Uniform

L^{1}

error bounds for semi-discrete finite element solutions of evolutionary integral equations

Lin, Qun ; Xu, Da ; Zhang, Shuhua

Applications of Mathematics 2012, GDML_Books, (2012), p. 144-162 / Harvested from

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Résumé

In this paper, we consider the second-order continuous time Galerkin approximation of the solution to the initial problem $u_{t} + \int_{0}^{t} β (t - s) A u (s) d s = 0, u (0) = v, t > 0,$ where A is an elliptic partial-differential operator and $β (t)$ is positive, nonincreasing and log-convex on $(0, \infty)$ with $0 \leq β (\infty) < β (0^{+}) \leq \infty$ . Error estimates are derived in the norm of $L_{t}^{1} (0, \infty; L_{x}^{2})$ , and some estimates for the first order time derivatives of the errors are also given.

MR MR3204408 | Zbl 1313.65336

EUDML-ID : urn:eudml:doc:287834
Mots clés:
Mots clés:

@article{702901,
     title = {Uniform $L^1$ error bounds for semi-discrete finite element solutions of evolutionary integral equations},
     booktitle = {Applications of Mathematics 2012},
     series = {GDML\_Books},
     publisher = {Institute of Mathematics AS CR},
     address = {Prague},
     year = {2012},
     pages = {144-162},
     mrnumber = {MR3204408},
     zbl = {1313.65336},
     url = {http://dml.mathdoc.fr/item/702901}
}

Lin, Qun; Xu, Da; Zhang, Shuhua. Uniform $L^1$ error bounds for semi-discrete finite element solutions of evolutionary integral equations, dans Applications of Mathematics 2012, GDML_Books,  (2012), pp. 144-162. http://gdmltest.u-ga.fr/item/702901/