{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T17:41:37Z","timestamp":1680284497846},"reference-count":26,"publisher":"Walter de Gruyter GmbH","issue":"1","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12001171"],"award-info":[{"award-number":["12001171"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006407","name":"Natural Science Foundation of Henan Province","doi-asserted-by":"publisher","award":["222300420550"],"award-info":[{"award-number":["222300420550"]}],"id":[{"id":"10.13039\/501100006407","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,1,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In this paper, we discuss the stability and error estimates of the fully discrete schemes for parabolic equations, in which local discontinuous Galerkin methods with generalized alternating numerical fluxes and a novel spectral deferred correction method based on second-order time integration methods are adopted.\nWith the energy techniques, we obtain both the second- and fourth-order spectral deferred correction time-marching with local discontinuous Galerkin spatial discretization are unconditional stable.\nThe optimal error estimates for the corresponding fully discrete scheme are derived by the aid of the generalized Gauss\u2013Radau projection.\nWe extend the analysis to problems with higher even-order derivatives.\nNumerical examples are displayed to verify our theoretical results.<\/jats:p>","DOI":"10.1515\/cmam-2022-0144","type":"journal-article","created":{"date-parts":[[2022,9,27]],"date-time":"2022-09-27T20:26:44Z","timestamp":1664310404000},"page":"277-296","source":"Crossref","is-referenced-by-count":0,"title":["Stability and Error Estimates of a Novel Spectral Deferred Correction Time-Marching with Local Discontinuous Galerkin Methods for Parabolic Equations"],"prefix":"10.1515","volume":"23","author":[{"given":"Lingling","family":"Zhou","sequence":"first","affiliation":[{"name":"School of Mathematics and Information Science , Henan Polytechnic University , Jiaozuo 454000, Henan , P. R. China"}]},{"given":"Wenhua","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Mathematics and Information Science , Henan Polytechnic University , Jiaozuo 454000, Henan , P. R. China"}]},{"given":"Ruihan","family":"Guo","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics , Zhengzhou University , Zhengzhou 450001, Henan , P. R. China"}]}],"member":"374","published-online":{"date-parts":[[2022,9,28]]},"reference":[{"key":"2023033112515566482_j_cmam-2022-0144_ref_001","doi-asserted-by":"crossref","unstructured":"U. M. Ascher, S. J. Ruuth and R. J. Spiteri,\nImplicit-explicit Runge\u2013Kutta methods for time-dependent partial differential equations,\nAppl. Numer. Math. 25 (1997), 151\u2013167.","DOI":"10.1016\/S0168-9274(97)00056-1"},{"key":"2023033112515566482_j_cmam-2022-0144_ref_002","doi-asserted-by":"crossref","unstructured":"F. Bassi and S. 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