A nonoverlapping domain decomposition iterative procedure is developed and analyzed for generalized Stokes problems and their finite element approximate problems in R^N（N=2,3）. The method is based on a mixed-type co...A nonoverlapping domain decomposition iterative procedure is developed and analyzed for generalized Stokes problems and their finite element approximate problems in R^N（N=2,3）. The method is based on a mixed-type consistency condition with two parameters as a transmission condition together with a derivative-free transmission data updating technique on the artificial interfaces. The method can be applied to a general multi-subdomain decomposition and implemented on parallel machines with local simple communications naturally.展开更多
In this paper,a new mixedfinite element scheme using element-wise stabilization is introduced for the biharmonic equation with variable coefficient on Lipschitz polyhedral domains.The proposed scheme doesn’t involve ...In this paper,a new mixedfinite element scheme using element-wise stabilization is introduced for the biharmonic equation with variable coefficient on Lipschitz polyhedral domains.The proposed scheme doesn’t involve any integration along mesh interfaces.The gradient of the solution is approximated by H(div)-conforming BDMk+1 element or vector valued Lagrange element with order k+1,while the solution is approximated by Lagrange element with order k+2 for any k≥0.This scheme can be easily implemented and produces symmetric and positive definite linear system.We provide a new discrete H^(2)-norm stability,which is useful not only in analysis of this scheme but also in C^(0) interior penalty methods and DG methods.Optimal convergences in both discrete H^(2)-norm and L^(2)-norm are derived.This scheme with its analysis is further generalized to the von K´arm´an equations.Finally,numerical results verifying the theoretical estimates of the proposed algorithms are also presented.展开更多
文摘A nonoverlapping domain decomposition iterative procedure is developed and analyzed for generalized Stokes problems and their finite element approximate problems in R^N（N=2,3）. The method is based on a mixed-type consistency condition with two parameters as a transmission condition together with a derivative-free transmission data updating technique on the artificial interfaces. The method can be applied to a general multi-subdomain decomposition and implemented on parallel machines with local simple communications naturally.
基金supported by the NSF of China(Grant No.12122115,11771363)supported by IITB Chair Professor’s fund and also partly by a MATRIX Grant No.MTR/201S/000309(SERB,DST,Govt.India)supported by a grant fromthe Research Grants Council of the Hong Kong Special Administrative Region,China(Project No.CityU 11302219).
文摘In this paper,a new mixedfinite element scheme using element-wise stabilization is introduced for the biharmonic equation with variable coefficient on Lipschitz polyhedral domains.The proposed scheme doesn’t involve any integration along mesh interfaces.The gradient of the solution is approximated by H(div)-conforming BDMk+1 element or vector valued Lagrange element with order k+1,while the solution is approximated by Lagrange element with order k+2 for any k≥0.This scheme can be easily implemented and produces symmetric and positive definite linear system.We provide a new discrete H^(2)-norm stability,which is useful not only in analysis of this scheme but also in C^(0) interior penalty methods and DG methods.Optimal convergences in both discrete H^(2)-norm and L^(2)-norm are derived.This scheme with its analysis is further generalized to the von K´arm´an equations.Finally,numerical results verifying the theoretical estimates of the proposed algorithms are also presented.
