@article {MR2358002,
    AUTHOR = {Bi, C. and Ginting, V.},
     TITLE = {Two-{G}rid {F}inite {V}olume {E}lement {M}ethod for {L}inear and {N}onlinear
              {E}lliptic {P}roblems},
  JOURNAL = {Numerische Mathematik},
    VOLUME = {108},
      YEAR = {2007},
    NUMBER = {2},
     PAGES = {177-198},
      ISSN = {0029-599X},
     CODEN = {NUMMA7},
   MRCLASS = {65N06},
  MRNUMBER = {2358002 (2008i:65227)},
MRREVIEWER = {Zheng Hui Xie},
       DOI = {10.1007/s00211-007-0115-9},
       URL = {http://dx.doi.org/10.1007/s00211-007-0115-9},
 ABSTRACT="Two-grid finite volume element discretization techniques, based on two linear conforming finite element spaces on one coarse and one fine grid, are presented for the two-dimensional second-order non-selfadjoint and indefinite linear elliptic problems and the two-dimensional second-order nonlinear elliptic problems. With the proposed techniques, solving the non-selfadjoint and indefinite elliptic problem on the fine space is reduced into solving a symmetric and positive definite elliptic problem on the fine space and solving the non-selfadjoint and indefinite elliptic problem on a much smaller space; solving a nonlinear elliptic problem on the fine space is reduced into solving a linear problem on the fine space and solving the nonlinear elliptic problem on a much smaller space. Convergence estimates are derived to justify the efficiency of the proposed two-grid algorithms. A set of numerical examples are presented to confirm the estimates."
}

{"_id":"M55vxeMTwnh4R9vqX","bibbaseid":"bi-ginting-twogridfinitevolumeelementmethodforlinearandnonlinearellipticproblems-2007","downloads":0,"creationDate":"2015-08-18T06:51:02.265Z","title":"Two-Grid Finite Volume Element Method for Linear and Nonlinear Elliptic Problems","author_short":["Bi, C.","Ginting, V."],"year":2007,"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":"Two-Grid Finite Volume Element Method for Linear and Nonlinear Elliptic Problems","journal":"Numerische Mathematik","volume":"108","year":"2007","number":"2","pages":"177-198","issn":"0029-599X","coden":"NUMMA7","mrclass":"65N06","mrnumber":"2358002 (2008i:65227)","mrreviewer":"Zheng Hui Xie","doi":"10.1007/s00211-007-0115-9","url":"http://dx.doi.org/10.1007/s00211-007-0115-9","abstract":"Two-grid finite volume element discretization techniques, based on two linear conforming finite element spaces on one coarse and one fine grid, are presented for the two-dimensional second-order non-selfadjoint and indefinite linear elliptic problems and the two-dimensional second-order nonlinear elliptic problems. With the proposed techniques, solving the non-selfadjoint and indefinite elliptic problem on the fine space is reduced into solving a symmetric and positive definite elliptic problem on the fine space and solving the non-selfadjoint and indefinite elliptic problem on a much smaller space; solving a nonlinear elliptic problem on the fine space is reduced into solving a linear problem on the fine space and solving the nonlinear elliptic problem on a much smaller space. Convergence estimates are derived to justify the efficiency of the proposed two-grid algorithms. A set of numerical examples are presented to confirm the estimates.","bibtex":"@article {MR2358002,\n AUTHOR = {Bi, C. and Ginting, V.},\n TITLE = {Two-{G}rid {F}inite {V}olume {E}lement {M}ethod for {L}inear and {N}onlinear\n {E}lliptic {P}roblems},\n JOURNAL = {Numerische Mathematik},\n VOLUME = {108},\n YEAR = {2007},\n NUMBER = {2},\n PAGES = {177-198},\n ISSN = {0029-599X},\n CODEN = {NUMMA7},\n MRCLASS = {65N06},\n MRNUMBER = {2358002 (2008i:65227)},\nMRREVIEWER = {Zheng Hui Xie},\n DOI = {10.1007/s00211-007-0115-9},\n URL = {http://dx.doi.org/10.1007/s00211-007-0115-9},\n ABSTRACT=\"Two-grid finite volume element discretization techniques, based on two linear conforming finite element spaces on one coarse and one fine grid, are presented for the two-dimensional second-order non-selfadjoint and indefinite linear elliptic problems and the two-dimensional second-order nonlinear elliptic problems. With the proposed techniques, solving the non-selfadjoint and indefinite elliptic problem on the fine space is reduced into solving a symmetric and positive definite elliptic problem on the fine space and solving the non-selfadjoint and indefinite elliptic problem on a much smaller space; solving a nonlinear elliptic problem on the fine space is reduced into solving a linear problem on the fine space and solving the nonlinear elliptic problem on a much smaller space. Convergence estimates are derived to justify the efficiency of the proposed two-grid algorithms. A set of numerical examples are presented to confirm the estimates.\"\n}\n\n","author_short":["Bi, C.","Ginting, V."],"key":"MR2358002","id":"MR2358002","bibbaseid":"bi-ginting-twogridfinitevolumeelementmethodforlinearandnonlinearellipticproblems-2007","role":"author","urls":{"Paper":"http://dx.doi.org/10.1007/s00211-007-0115-9"},"metadata":{"authorlinks":{"ginting, v":"https://bibbase.org/show?bib=https://bibbase.org/network/files/3yQtKfRddpmAbuCJN&msg=preview&fileId=3yQtKfRddpmAbuCJN"}},"downloads":0},"search_terms":["two","grid","finite","volume","element","method","linear","nonlinear","elliptic","problems","bi","ginting"],"keywords":[],"authorIDs":["KGv5qNX2wproMHaMz"],"dataSources":["FMKDotGw9QMpa9Abz","x4GJj42ibi69jHYvw"]}