This paper proves the asymptotic behaviour for a class of reaction-diffusionsystem in bacteriology by using duality technique, semigroup theorem, Lp--estimates andupper and lower solutions method.
Four primal discontinuous Galerkin methods are applied to solve reactive transport problems, namely, Oden-BabuSka-Baumann DG （OBB-DG）, non-symmetric interior penalty Galerkin （NIPG）, symmetric interior penalty Gal...Four primal discontinuous Galerkin methods are applied to solve reactive transport problems, namely, Oden-BabuSka-Baumann DG （OBB-DG）, non-symmetric interior penalty Galerkin （NIPG）, symmetric interior penalty Galerkin （SIPG）, and incomplete interior penalty Galerkin （IIPG）. A unified a posteriori residual-type error estimation is derived explicitly for these methods. From the computed solution and given data, explicit estimators can be computed efficiently and directly, which can be used as error indicators for adaptation. Unlike in the reference [10], we obtain the error estimators in L^2 （L^2） norm by using duality techniques instead of in L^2（H^1） norm.展开更多
In order to obtain an expected numerical solution, a fully discrete discontinuous Galerkin method is applied to a kind of reactive transport problems in two dimension. That is to say, the space variable is discretized...In order to obtain an expected numerical solution, a fully discrete discontinuous Galerkin method is applied to a kind of reactive transport problems in two dimension. That is to say, the space variable is discretized with the symmetric interior penalty Calerkin method （SIPG）, and the time variable is done with the backward Euler method. Making use of the duality technique, hp approximation properties and the interpolation theory, a residual-type a posteriori error estimation is achieved, which can be used for adaptivity. Compared with the analyses of semi-discretization, the current presentation is more challenging and more significant.展开更多
文摘This paper proves the asymptotic behaviour for a class of reaction-diffusionsystem in bacteriology by using duality technique, semigroup theorem, Lp--estimates andupper and lower solutions method.
基金This work is supported by Program for New Century Excellent Talents in University of China State Education Ministry NCET-04-0776, National Science Foundation of China, the National Basic Research Program under the Grant 2005CB321703, and the key project of China State Education Ministry and Hunan Education Commission.
文摘Four primal discontinuous Galerkin methods are applied to solve reactive transport problems, namely, Oden-BabuSka-Baumann DG （OBB-DG）, non-symmetric interior penalty Galerkin （NIPG）, symmetric interior penalty Galerkin （SIPG）, and incomplete interior penalty Galerkin （IIPG）. A unified a posteriori residual-type error estimation is derived explicitly for these methods. From the computed solution and given data, explicit estimators can be computed efficiently and directly, which can be used as error indicators for adaptation. Unlike in the reference [10], we obtain the error estimators in L^2 （L^2） norm by using duality techniques instead of in L^2（H^1） norm.
基金supported by Hunan Provincial Natural Science Foundation of China under Grant No. 10JJ3021Scientific Research Fund of Hunan Provincial Education Department under Grant No.11B032the Planned Science and Technology Project of Hunan Province and Aid program for Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province
文摘In order to obtain an expected numerical solution, a fully discrete discontinuous Galerkin method is applied to a kind of reactive transport problems in two dimension. That is to say, the space variable is discretized with the symmetric interior penalty Calerkin method （SIPG）, and the time variable is done with the backward Euler method. Making use of the duality technique, hp approximation properties and the interpolation theory, a residual-type a posteriori error estimation is achieved, which can be used for adaptivity. Compared with the analyses of semi-discretization, the current presentation is more challenging and more significant.
