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. ![A Posteriori Error Estimates of Discontinuous Galerkin Method for Nonmonotone Quasi-Linear Elliptic Problems [link]](https://bibbase.org/img/filetypes/link.svg "link")
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."
}
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