A Posteriori Error Estimates of Discontinuous Galerkin Method for Nonmonotone Quasi-Linear Elliptic Problems. Bi, C. & Ginting, V. Journal of Scientific Computing, 55(3):659-687, 2013.
Paper doi abstract bibtex In this paper, we propose and study the residual-based a posteriori error estimates of h-version of symmetric interior penalty discontinuous Galerkin method for solving a class of second order quasi-linear elliptic problems which are of nonmonotone type. Computable upper and lower bounds on the error measured in terms of a natural mesh-dependent energy norm and the broken H 1-seminorm, respectively, are derived. Numerical experiments are also provided to illustrate the performance of the proposed estimators.
@article {MR3045707,
AUTHOR = {Bi, C. and Ginting, V.},
TITLE = {A {P}osteriori {E}rror {E}stimates of {D}iscontinuous {G}alerkin
{M}ethod for {N}onmonotone {Q}uasi-{L}inear {E}lliptic {P}roblems},
JOURNAL = {Journal of Scientific Computing},
VOLUME = {55},
YEAR = {2013},
NUMBER = {3},
PAGES = {659-687},
ISSN = {0885-7474},
CODEN = {JSCOEB},
MRCLASS = {65N30 (65N15)},
MRNUMBER = {3045707},
MRREVIEWER = {Igor Bock},
DOI = {10.1007/s10915-012-9651-2},
URL = {http://dx.doi.org/10.1007/s10915-012-9651-2},
ABSTRACT="In this paper, we propose and study the residual-based a posteriori error estimates of h-version of symmetric interior penalty discontinuous Galerkin method for solving a class of second order quasi-linear elliptic problems which are of nonmonotone type. Computable upper and lower bounds on the error measured in terms of a natural mesh-dependent energy norm and the broken H 1-seminorm, respectively, are derived. Numerical experiments are also provided to illustrate the performance of the proposed estimators."
}
Downloads: 0
{"_id":"mT7viimy2TuDjz8pv","authorIDs":["5517e0768039785715000223","5dee6cf9773914de01000191","5defe7cd14db5cdf01000040","5df7a3daf3cb28df0100010d","5dfdf9d8935a0ade01000025","5e5be5eed49321e001000011","7QXiBuTATxo5D68DC","8u4nAZBX3Nvkm5uWQ","9h2mJwBD8fwHxQzN4","EETZPEkFzmbXGbtqj","KGv5qNX2wproMHaMz","P2b2rK9qBBgTnheZ2","WRpBGdMW5fvCQ7yfS","bDRwyrDc8KKyFjHQQ","vSZhCTKZWihxepL88"],"author_short":["Bi, C.","Ginting, V."],"bibbaseid":"bi-ginting-aposteriorierrorestimatesofdiscontinuousgalerkinmethodfornonmonotonequasilinearellipticproblems-2013","bibdata":{"bibtype":"article","type":"article","author":[{"propositions":[],"lastnames":["Bi"],"firstnames":["C."],"suffixes":[]},{"propositions":[],"lastnames":["Ginting"],"firstnames":["V."],"suffixes":[]}],"title":"A Posteriori Error Estimates of Discontinuous Galerkin Method for Nonmonotone Quasi-Linear Elliptic Problems","journal":"Journal of Scientific Computing","volume":"55","year":"2013","number":"3","pages":"659-687","issn":"0885-7474","coden":"JSCOEB","mrclass":"65N30 (65N15)","mrnumber":"3045707","mrreviewer":"Igor Bock","doi":"10.1007/s10915-012-9651-2","url":"http://dx.doi.org/10.1007/s10915-012-9651-2","abstract":"In this paper, we propose and study the residual-based a posteriori error estimates of h-version of symmetric interior penalty discontinuous Galerkin method for solving a class of second order quasi-linear elliptic problems which are of nonmonotone type. Computable upper and lower bounds on the error measured in terms of a natural mesh-dependent energy norm and the broken H 1-seminorm, respectively, are derived. Numerical experiments are also provided to illustrate the performance of the proposed estimators.","bibtex":"@article {MR3045707,\n AUTHOR = {Bi, C. and Ginting, V.},\n TITLE = {A {P}osteriori {E}rror {E}stimates of {D}iscontinuous {G}alerkin\n {M}ethod for {N}onmonotone {Q}uasi-{L}inear {E}lliptic {P}roblems},\n JOURNAL = {Journal of Scientific Computing},\n VOLUME = {55},\n YEAR = {2013},\n NUMBER = {3},\n PAGES = {659-687},\n ISSN = {0885-7474},\n CODEN = {JSCOEB},\n MRCLASS = {65N30 (65N15)},\n MRNUMBER = {3045707},\nMRREVIEWER = {Igor Bock},\n DOI = {10.1007/s10915-012-9651-2},\n URL = {http://dx.doi.org/10.1007/s10915-012-9651-2},\n ABSTRACT=\"In this paper, we propose and study the residual-based a posteriori error estimates of h-version of symmetric interior penalty discontinuous Galerkin method for solving a class of second order quasi-linear elliptic problems which are of nonmonotone type. Computable upper and lower bounds on the error measured in terms of a natural mesh-dependent energy norm and the broken H 1-seminorm, respectively, are derived. Numerical experiments are also provided to illustrate the performance of the proposed estimators.\"\n}\n\n","author_short":["Bi, C.","Ginting, V."],"key":"MR3045707","id":"MR3045707","bibbaseid":"bi-ginting-aposteriorierrorestimatesofdiscontinuousgalerkinmethodfornonmonotonequasilinearellipticproblems-2013","role":"author","urls":{"Paper":"http://dx.doi.org/10.1007/s10915-012-9651-2"},"metadata":{"authorlinks":{"ginting, v":"https://bibbase.org/show?bib=https://bibbase.org/network/files/3yQtKfRddpmAbuCJN&msg=preview&fileId=3yQtKfRddpmAbuCJN"}},"downloads":0},"bibtype":"article","biburl":"https://bibbase.org/network/files/3yQtKfRddpmAbuCJN","creationDate":"2015-03-29T11:22:30.079Z","downloads":0,"keywords":[],"search_terms":["posteriori","error","estimates","discontinuous","galerkin","method","nonmonotone","quasi","linear","elliptic","problems","bi","ginting"],"title":"A Posteriori Error Estimates of Discontinuous Galerkin Method for Nonmonotone Quasi-Linear Elliptic Problems","year":2013,"dataSources":["FMKDotGw9QMpa9Abz","x4GJj42ibi69jHYvw"]}