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For the derived semi-discrete finite element spatial discretization scheme, the a priori bounds are given that does not rely on the mesh width restriction. Further, with the help of the a priori error bounds of the Stokes and Ritz projections, optimal error estimates for the velocity, the conformation tensor and the pressure are presented, respectively. Finally, in order to implement the proposed semi-discrete numerical scheme, we derive three kinds of fully discrete schemes, e.g., Newton\u2019s iterative scheme, Picard\u2019s iterative scheme and implicit-explicit time-stepping scheme. Finally, several numerical experiments are conducted to confirm our theoretical results.<\/jats:p>","DOI":"10.1515\/cmam-2017-0021","type":"journal-article","created":{"date-parts":[[2017,7,6]],"date-time":"2017-07-06T10:01:41Z","timestamp":1499335301000},"page":"275-296","source":"Crossref","is-referenced-by-count":11,"title":["Semi-Discrete Galerkin Finite Element Method for the Diffusive Peterlin Viscoelastic Model"],"prefix":"10.1515","volume":"18","author":[{"given":"Yao-Lin","family":"Jiang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics , Xi\u2019an Jiaotong University , Xi\u2019an 710049 , P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yun-Bo","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics , Xi\u2019an Jiaotong University , Xi\u2019an 710049 , P. R. 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