Optimal \(L_{2}\) estimates for semidiscrete Galerkin method applied to parabolic integro-differential equations with nonsmooth data
Pani, Amiya Kumar ; Goswami, Deepjyoti ; Yadav, Sangita
ANZIAM Journal, Tome 55 (2014), / Harvested from Australian Mathematical Society
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We propose and analyse an alternate approach to a priori error estimates for the semidiscrete Galerkin approximation to a time-dependent parabolic integro-differential equation with nonsmooth initial data. The method is based on energy arguments combined with repeated use of time integration, but without using parabolic-type duality techniques. An optimal \(L_{2}\)-error estimate is derived for the semidiscrete approximation when the initial data is in \(L_{2}\). A superconvergence result is obtained and then used to prove a maximum norm estimate for parabolic integro-differential equations defined on a two-dimensional bounded domain. doi:10.1017/S1446181114000030

Publié le : 2014-01-01
DOI : https://doi.org/10.21914/anziamj.v55i0.5522 
@article{5522,
     title = {Optimal \(L\_{2}\) estimates for semidiscrete Galerkin method applied to parabolic integro-differential equations with nonsmooth data},
     journal = {ANZIAM Journal},
     volume = {55},
     year = {2014},
     doi = {10.21914/anziamj.v55i0.5522},
     language = {EN},
     url = {http://dml.mathdoc.fr/item/5522}
}

Pani, Amiya Kumar; Goswami, Deepjyoti; Yadav, Sangita. Optimal \(L_{2}\) estimates for semidiscrete Galerkin method applied to parabolic integro-differential equations with nonsmooth data. ANZIAM Journal, Tome 55 (2014) . doi : 10.21914/anziamj.v55i0.5522. http://gdmltest.u-ga.fr/item/5522/