{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T07:59:13Z","timestamp":1649145553318},"reference-count":29,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Model. Simul. Sci. Comput."],"published-print":{"date-parts":[[2014,3]]},"abstract":"<jats:p> In this paper, a new numerical method based on a new expanded mixed scheme and the characteristic method is developed and discussed for Sobolev equation with convection term. The hyperbolic part [Formula: see text] is handled by the characteristic method and the diffusion term \u2207 \u22c5 (a(x, t)\u2207u+b(x, t)\u2207u<jats:sub>t<\/jats:sub>) is approximated by the new expanded mixed method, whose gradient belongs to the simple square integrable (L<jats:sup>2<\/jats:sup>(\u03a9))<jats:sup>2<\/jats:sup> space instead of the classical H( div ; \u03a9) space. For a priori error estimates, some important lemmas based on the new expanded mixed projection are introduced. An optimal priori error estimates in L<jats:sup>2<\/jats:sup>-norm for the scalar unknown u and a priori error estimates in (L<jats:sup>2<\/jats:sup>)<jats:sup>2<\/jats:sup>-norm for its gradient \u03bb, and its flux \u03c3 (the coefficients times the negative gradient) are derived. In particular, an optimal priori error estimate in H<jats:sup>1<\/jats:sup>-norm for the scalar unknown u is obtained. <\/jats:p>","DOI":"10.1142\/s1793962313500153","type":"journal-article","created":{"date-parts":[[2013,4,5]],"date-time":"2013-04-05T06:02:19Z","timestamp":1365141739000},"page":"1350015","source":"Crossref","is-referenced-by-count":1,"title":["A NEW CHARACTERISTIC EXPANDED MIXED METHOD FOR SOBOLEV EQUATION WITH CONVECTION TERM"],"prefix":"10.1142","volume":"05","author":[{"given":"YANG","family":"LIU","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"HONG","family":"LI","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"SIRIGULENG","family":"HE","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ZHICHAO","family":"FANG","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"JINFENG","family":"WANG","sequence":"additional","affiliation":[{"name":"School of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Hohhot 010070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2013,12,25]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(92)90074-N"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/s10255-007-7065-y"},{"key":"rf3","first-page":"3176","volume":"218","author":"Shi D. 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