The purpose of the current article is to study the H^(1)-stability for all positive time of the linearly extrapolated BDF2 timestepping scheme for the magnetohydrodynamics and Boussinesq equations.Specifically,we disc...The purpose of the current article is to study the H^(1)-stability for all positive time of the linearly extrapolated BDF2 timestepping scheme for the magnetohydrodynamics and Boussinesq equations.Specifically,we discretize in time using the linearly backward differentiation formula,and by employing both the discrete Gronwall lemma and the discrete uniform Gronwall lemma,we establish that each numerical scheme is uniformly bounded in the H^(1)-norm.展开更多
We analyze an h-p version Petrov-Galerkin finite element method for linear Volterra integrodifferential equations. We prove optimal a priori error bounds in the L2- and H1-norm that are explicit in the time steps,the ...We analyze an h-p version Petrov-Galerkin finite element method for linear Volterra integrodifferential equations. We prove optimal a priori error bounds in the L2- and H1-norm that are explicit in the time steps,the approximation orders and in the regularity of the exact solution. Numerical experiments confirm the theoretical results. Moreover,we observe that the numerical scheme superconverges at the nodal points of the time partition.展开更多
文摘The purpose of the current article is to study the H^(1)-stability for all positive time of the linearly extrapolated BDF2 timestepping scheme for the magnetohydrodynamics and Boussinesq equations.Specifically,we discretize in time using the linearly backward differentiation formula,and by employing both the discrete Gronwall lemma and the discrete uniform Gronwall lemma,we establish that each numerical scheme is uniformly bounded in the H^(1)-norm.
基金supported by National Natural Science Foundation of China(Grant Nos.11226330 and 11301343)the Research Fund for the Doctoral Program of Higher Education of China(Grant No.20113127120002)+3 种基金the Research Fund for Young Teachers Program in Shanghai(GrantNo.shsf018)the Fund for E-institute of Shanghai Universities(Grant No.E03004)supported by the Natural Sciences and Engineering Research Council of Canada(Grant No.OGP0046726)Shanghai University under Leading Academic Discipline Project of Shanghai MunicipalEducation Commission(Grant No.J50101)
文摘We analyze an h-p version Petrov-Galerkin finite element method for linear Volterra integrodifferential equations. We prove optimal a priori error bounds in the L2- and H1-norm that are explicit in the time steps,the approximation orders and in the regularity of the exact solution. Numerical experiments confirm the theoretical results. Moreover,we observe that the numerical scheme superconverges at the nodal points of the time partition.
