In the paper,an inf-sup stabilized finite element method by multiscale functions for the Stokes equations is discussed.The key idea is to use a PetrovGalerkin approach based on the enrichment of the standard polynomi...In the paper,an inf-sup stabilized finite element method by multiscale functions for the Stokes equations is discussed.The key idea is to use a PetrovGalerkin approach based on the enrichment of the standard polynomial space for the velocity component with multiscale functions.The inf-sup condition for P_(1)-P_(0)triangular element(or Q_(1)-P_(0)quadrilateral element)is established.The optimal error estimates of the stabilized finite element method for the Stokes equations are obtained.展开更多
We consider a previously proposed general nonlinear poromechanical formulation, and we derive a linearized version of this model. For this linearized model, we obtain an existence result and we propose a complete disc...We consider a previously proposed general nonlinear poromechanical formulation, and we derive a linearized version of this model. For this linearized model, we obtain an existence result and we propose a complete discretization strategy – in time and space – with a special concern for issues associated with incompressible or nearly-incompressible behavior. We provide a detailed mathematical analysis of this strategy,the main result being an error estimate uniform with respect to the compressibility parameter. We then illustrate our approach with detailed simulation results and we numerically investigate the importance of the assumptions made in the analysis, including the fulfillment of specific inf-sup conditions.展开更多
基金the support of the Natural Science Foundation of China(No.10671154)the National Basic Research Program(No.2005CB321703)。
文摘In the paper,an inf-sup stabilized finite element method by multiscale functions for the Stokes equations is discussed.The key idea is to use a PetrovGalerkin approach based on the enrichment of the standard polynomial space for the velocity component with multiscale functions.The inf-sup condition for P_(1)-P_(0)triangular element(or Q_(1)-P_(0)quadrilateral element)is established.The optimal error estimates of the stabilized finite element method for the Stokes equations are obtained.
文摘We consider a previously proposed general nonlinear poromechanical formulation, and we derive a linearized version of this model. For this linearized model, we obtain an existence result and we propose a complete discretization strategy – in time and space – with a special concern for issues associated with incompressible or nearly-incompressible behavior. We provide a detailed mathematical analysis of this strategy,the main result being an error estimate uniform with respect to the compressibility parameter. We then illustrate our approach with detailed simulation results and we numerically investigate the importance of the assumptions made in the analysis, including the fulfillment of specific inf-sup conditions.
基金The National Natural Science Foundation of China(1097116511001216+4 种基金1107119310871156)the National High-Tech Research and Development Program of China(2009AA01A135)the Foundation of AVIC Chengdu Aircraft Design and Research Institutethe Science Research Foundation of SNEDU(2010JK560)
基金The National Natural Science Foundation of China(1097120311271340)+2 种基金the Research Fund for the Doctoral Program of Higher Education of China(20094101110006)the Youth Development Foundation of Shangqiu Normal University(2010QN013)the JSPS Innovation Program(CXZZ110134)
