A finite element method for time fractional partial differential equations

%0 Journal Article
%1 ford2011finite
%A Ford, Neville J.
%A Xiao, Jingyu
%A Yan, Yubin
%D 2011
%J Fractional Calculus and Applied Analysis
%K 35r11-fractional-partial-differential-equations 45k05-integro-partial-differential-equations 65m12-pdes-ivps-stability-and-convergence-of-numerical-methods 65m15-pdes-ivps-error-bounds 65m60-pdes-ibvps-finite-elements 65r20-numerical-analysis-integral-equations
%N 3
%P 454–474
%R 10.2478/s13540-011-0028-2
%T A finite element method for time fractional partial differential equations
%U link.springer.com/article/10.2478/s13540-011-0028-2
%V 14
%X In this paper, we consider the finite element method for time fractional partial differential equations. The existence and uniqueness of the solutions are proved by using the Lax-Milgram Lemma. A time stepping method is introduced based on a quadrature formula approach. The fully discrete scheme is considered by using a finite element method and optimal convergence error estimates are obtained. The numerical examples at the end of the paper show that the experimental results are consistent with our theoretical results.

@article{ford2011finite,
abstract = {In this paper, we consider the finite element method for time fractional partial differential equations. The existence and uniqueness of the solutions are proved by using the Lax-Milgram Lemma. A time stepping method is introduced based on a quadrature formula approach. The fully discrete scheme is considered by using a finite element method and optimal convergence error estimates are obtained. The numerical examples at the end of the paper show that the experimental results are consistent with our theoretical results.},
added-at = {2024-07-03T01:59:10.000+0200},
author = {Ford, Neville J. and Xiao, Jingyu and Yan, Yubin},
biburl = {https://www.bibsonomy.org/bibtex/281f70e549fab289f54df8462c4418cd2/gdmcbain},
doi = {10.2478/s13540-011-0028-2},
fjournal = {Fractional Calculus \& Applied Analysis},
interhash = {e0c31cd7d9532e6bd59f1dd490958db4},
intrahash = {81f70e549fab289f54df8462c4418cd2},
issn = {1311-0454},
journal = {Fractional Calculus and Applied Analysis},
keywords = {35r11-fractional-partial-differential-equations 45k05-integro-partial-differential-equations 65m12-pdes-ivps-stability-and-convergence-of-numerical-methods 65m15-pdes-ivps-error-bounds 65m60-pdes-ibvps-finite-elements 65r20-numerical-analysis-integral-equations},
language = {en},
number = 3,
pages = {454–474},
timestamp = {2024-07-03T01:59:10.000+0200},
title = {A finite element method for time fractional partial differential equations},
url = {https://link.springer.com/article/10.2478/s13540-011-0028-2},
volume = 14,
year = 2011,
zbl = {1273.65142},
zbmath = {6217555}
}