This paper is concerned with the finite element scheme and the alternating direction finite element scheme for some nonlinear reaction - diffusion systems with the second or the third boundary value conditions. Not on...This paper is concerned with the finite element scheme and the alternating direction finite element scheme for some nonlinear reaction - diffusion systems with the second or the third boundary value conditions. Not only the existence and uniqueness of solutions for these approximational schemes are obtained, but also the optimal H1 - norm and L2- norm error estimate results are demonstrated.展开更多
A family of stable mixed finite elements for the linear elasticity on tetrahedral grids are constructed,where the stress is approximated by symmetric H(div)-Pk polynomial tensors and the displacement is approximated b...A family of stable mixed finite elements for the linear elasticity on tetrahedral grids are constructed,where the stress is approximated by symmetric H(div)-Pk polynomial tensors and the displacement is approximated by C-1-Pk-1polynomial vectors,for all k 4.The main ingredients for the analysis are a new basis of the space of symmetric matrices,an intrinsic H(div)bubble function space on each element,and a new technique for establishing the discrete inf-sup condition.In particular,they enable us to prove that the divergence space of the H(div)bubble function space is identical to the orthogonal complement space of the rigid motion space with respect to the vector-valued Pk-1polynomial space on each tetrahedron.The optimal error estimate is proved,verified by numerical examples.展开更多
文摘This paper is concerned with the finite element scheme and the alternating direction finite element scheme for some nonlinear reaction - diffusion systems with the second or the third boundary value conditions. Not only the existence and uniqueness of solutions for these approximational schemes are obtained, but also the optimal H1 - norm and L2- norm error estimate results are demonstrated.
基金supported by National Natural Science Foundation of China(Grant Nos.11271035,91430213 and 11421101)
文摘A family of stable mixed finite elements for the linear elasticity on tetrahedral grids are constructed,where the stress is approximated by symmetric H(div)-Pk polynomial tensors and the displacement is approximated by C-1-Pk-1polynomial vectors,for all k 4.The main ingredients for the analysis are a new basis of the space of symmetric matrices,an intrinsic H(div)bubble function space on each element,and a new technique for establishing the discrete inf-sup condition.In particular,they enable us to prove that the divergence space of the H(div)bubble function space is identical to the orthogonal complement space of the rigid motion space with respect to the vector-valued Pk-1polynomial space on each tetrahedron.The optimal error estimate is proved,verified by numerical examples.
