@article {MR2832790,
    AUTHOR = {Bi, C. and Ginting, V.},
     TITLE = {Finite-{V}olume-{E}lement {M}ethod for {S}econd-{O}rder {Q}uasilinear
              {E}lliptic {P}roblems},
  JOURNAL = {IMA Journal of Numerical Analysis},
    VOLUME = {31},
      YEAR = {2011},
    NUMBER = {3},
     PAGES = {1062-1089},
      ISSN = {0272-4979},
     CODEN = {IJNADN},
   MRCLASS = {65N08 (35J25 35J62 65N12 65N15 65N30)},
  MRNUMBER = {2832790 (2012j:65367)},
MRREVIEWER = {Veronika Sobot{\'{\i}}kov{\'a}},
       DOI = {10.1093/imanum/drq011},
       URL = {http://dx.doi.org/10.1093/imanum/drq011},
ABSTRACT="In this paper we consider the finite-volume-element method for general second-order quasilinear elliptic problems over a convex polygonal domain in the plane. Using reasonable assumptions, we show the existence and uniqueness of the finite-volume-element approximations. It is proved that the finite-volume-element approximations are convergent with Graphic, where r > 2, and Graphic in the H1-, W1, �- and L2-norms, respectively, for u ? W2, r(�) and u ? W2, �(�) ? W3, p(�), where p > 1. Moreover, the optimal-order error estimates in the W1, �- and L2-norms and an Graphic estimate in the L�-norm are derived under the assumption that u ? W2, �(�) ? H3(�). Numerical experiments are presented to confirm the estimates."
}

{"_id":"2KHZe8CNAxy8AZJAH","bibbaseid":"bi-ginting-finitevolumeelementmethodforsecondorderquasilinearellipticproblems-2011","downloads":0,"creationDate":"2015-08-18T06:51:02.218Z","title":"Finite-Volume-Element Method for Second-Order Quasilinear Elliptic Problems","author_short":["Bi, C.","Ginting, V."],"year":2011,"bibtype":"article","biburl":"https://bibbase.org/network/files/3yQtKfRddpmAbuCJN","bibdata":{"bibtype":"article","type":"article","author":[{"propositions":[],"lastnames":["Bi"],"firstnames":["C."],"suffixes":[]},{"propositions":[],"lastnames":["Ginting"],"firstnames":["V."],"suffixes":[]}],"title":"Finite-Volume-Element Method for Second-Order Quasilinear Elliptic Problems","journal":"IMA Journal of Numerical Analysis","volume":"31","year":"2011","number":"3","pages":"1062-1089","issn":"0272-4979","coden":"IJNADN","mrclass":"65N08 (35J25 35J62 65N12 65N15 65N30)","mrnumber":"2832790 (2012j:65367)","mrreviewer":"Veronika Sobotíková","doi":"10.1093/imanum/drq011","url":"http://dx.doi.org/10.1093/imanum/drq011","abstract":"In this paper we consider the finite-volume-element method for general second-order quasilinear elliptic problems over a convex polygonal domain in the plane. Using reasonable assumptions, we show the existence and uniqueness of the finite-volume-element approximations. It is proved that the finite-volume-element approximations are convergent with Graphic, where r > 2, and Graphic in the H1-, W1, �- and L2-norms, respectively, for u ? W2, r(�) and u ? W2, �(�) ? W3, p(�), where p > 1. Moreover, the optimal-order error estimates in the W1, �- and L2-norms and an Graphic estimate in the L�-norm are derived under the assumption that u ? W2, �(�) ? H3(�). Numerical experiments are presented to confirm the estimates.","bibtex":"@article {MR2832790,\n AUTHOR = {Bi, C. and Ginting, V.},\n TITLE = {Finite-{V}olume-{E}lement {M}ethod for {S}econd-{O}rder {Q}uasilinear\n {E}lliptic {P}roblems},\n JOURNAL = {IMA Journal of Numerical Analysis},\n VOLUME = {31},\n YEAR = {2011},\n NUMBER = {3},\n PAGES = {1062-1089},\n ISSN = {0272-4979},\n CODEN = {IJNADN},\n MRCLASS = {65N08 (35J25 35J62 65N12 65N15 65N30)},\n MRNUMBER = {2832790 (2012j:65367)},\nMRREVIEWER = {Veronika Sobot{\\'{\\i}}kov{\\'a}},\n DOI = {10.1093/imanum/drq011},\n URL = {http://dx.doi.org/10.1093/imanum/drq011},\nABSTRACT=\"In this paper we consider the finite-volume-element method for general second-order quasilinear elliptic problems over a convex polygonal domain in the plane. Using reasonable assumptions, we show the existence and uniqueness of the finite-volume-element approximations. It is proved that the finite-volume-element approximations are convergent with Graphic, where r > 2, and Graphic in the H1-, W1, �- and L2-norms, respectively, for u ? W2, r(�) and u ? W2, �(�) ? W3, p(�), where p > 1. Moreover, the optimal-order error estimates in the W1, �- and L2-norms and an Graphic estimate in the L�-norm are derived under the assumption that u ? W2, �(�) ? H3(�). Numerical experiments are presented to confirm the estimates.\"\n}\n\n","author_short":["Bi, C.","Ginting, V."],"key":"MR2832790","id":"MR2832790","bibbaseid":"bi-ginting-finitevolumeelementmethodforsecondorderquasilinearellipticproblems-2011","role":"author","urls":{"Paper":"http://dx.doi.org/10.1093/imanum/drq011"},"metadata":{"authorlinks":{"ginting, v":"https://bibbase.org/show?bib=https://bibbase.org/network/files/3yQtKfRddpmAbuCJN&msg=preview&fileId=3yQtKfRddpmAbuCJN"}},"downloads":0},"search_terms":["finite","volume","element","method","second","order","quasilinear","elliptic","problems","bi","ginting"],"keywords":[],"authorIDs":["KGv5qNX2wproMHaMz"],"dataSources":["FMKDotGw9QMpa9Abz","x4GJj42ibi69jHYvw"]}