The global boundness and existence are presented for the kind of the Rosseland equation with a general growth condition. A linearized map in a closed convex set is defined. The image set is precompact, and thus a fixe...The global boundness and existence are presented for the kind of the Rosseland equation with a general growth condition. A linearized map in a closed convex set is defined. The image set is precompact, and thus a fixed point exists. A multi-scale expansion method is used to obtain the homogenized equation. This equation satisfies a similar growth condition.展开更多
We characterize non-finitely generated soluble groups with the maximalcondition on non-Baer subgroups and prove that a non-Baer soluble group is a Cernikov group or ithas an infinite properly descending series of non-...We characterize non-finitely generated soluble groups with the maximalcondition on non-Baer subgroups and prove that a non-Baer soluble group is a Cernikov group or ithas an infinite properly descending series of non-Baer subgroups.展开更多
In this paper, we study the explicit expressions of the constants in the error estimates of the lowest order mixed and nonconforming finite element methods. We start with an explicit relation between the error constan...In this paper, we study the explicit expressions of the constants in the error estimates of the lowest order mixed and nonconforming finite element methods. We start with an explicit relation between the error constant of the lowest order Raviart-Thomas interpolation error and the geometric characters of the triangle. This gives an explicit error constant of the lowest order mixed finite element method. Furthermore, similar results can be ex- tended to the nonconforming P1 scheme based on its close connection with the lowest order Raviart-Thomas method. Meanwhile, such explicit a priori error estimates can be used as computable error bounds, which are also consistent with the maximal angle condition for the optimal error estimates of mixed and nonconforming finite element methods.展开更多
基金Supported by the National Basic Research Program of China(973 Program)(No.2012CB025904)the National Natural Science Foundation of China(No.90916027)
文摘The global boundness and existence are presented for the kind of the Rosseland equation with a general growth condition. A linearized map in a closed convex set is defined. The image set is precompact, and thus a fixed point exists. A multi-scale expansion method is used to obtain the homogenized equation. This equation satisfies a similar growth condition.
文摘We characterize non-finitely generated soluble groups with the maximalcondition on non-Baer subgroups and prove that a non-Baer soluble group is a Cernikov group or ithas an infinite properly descending series of non-Baer subgroups.
基金supported by the Special Funds for Major State Basic Research Project(No.2005CB321701)
文摘In this paper, we study the explicit expressions of the constants in the error estimates of the lowest order mixed and nonconforming finite element methods. We start with an explicit relation between the error constant of the lowest order Raviart-Thomas interpolation error and the geometric characters of the triangle. This gives an explicit error constant of the lowest order mixed finite element method. Furthermore, similar results can be ex- tended to the nonconforming P1 scheme based on its close connection with the lowest order Raviart-Thomas method. Meanwhile, such explicit a priori error estimates can be used as computable error bounds, which are also consistent with the maximal angle condition for the optimal error estimates of mixed and nonconforming finite element methods.
