In this article,we propose a new finite element spaceΛh for the expanded mixed finite element method(EMFEM)for second-order elliptic problems to guarantee its computing capability and reduce the computation cost.The ...In this article,we propose a new finite element spaceΛh for the expanded mixed finite element method(EMFEM)for second-order elliptic problems to guarantee its computing capability and reduce the computation cost.The new finite element spaceΛh is designed in such a way that the strong requirement V h⊂Λh in[9]is weakened to{v h∈V h;d i v v h=0}⊂Λh so that it needs fewer degrees of freedom than its classical counterpart.Furthermore,the newΛh coupled with the Raviart-Thomas space satisfies the inf-sup condition,which is crucial to the computation of mixed methods for its close relation to the behavior of the smallest nonzero eigenvalue of the stiff matrix,and thus the existence,uniqueness and optimal approximate capability of the EMFEM solution are proved for rectangular partitions in R d,d=2,3 and for triangular partitions in R 2.Also,the solvability of the EMFEM for triangular partition in R 3 can be directly proved without the inf-sup condition.Numerical experiments are conducted to confirm these theoretical findings.展开更多
A reduced-order extrapolation algorithm based on Crank-Nicolson least-squares mixed finite element （CNLSMFE） formulation and proper orthogonal decomposition （POD） technique for two-dimensional （2D） Sobolev equat...A reduced-order extrapolation algorithm based on Crank-Nicolson least-squares mixed finite element （CNLSMFE） formulation and proper orthogonal decomposition （POD） technique for two-dimensional （2D） Sobolev equations is established. The error estimates of the reduced-order CNLSMFE solutions and the implementation for the reduced-order extrapolation algorithm are provided. A numerical example is used to show that the results of numerical computations are consistent with theoretical conclusions. Moreover, it is shown that the reduced-order extrapolation algorithm is feasible and efficient for seeking numerical solutions to 2D Sobolev equations.展开更多
基金supported by NSF of China grant 11971276H.Chen was supported by NSF of China grants 12171287,10971254 and 11471196+1 种基金H.Wang was supported by the ARO MURI Grant W911NF-15-1-0562by the National Science Foundation under Grant DMS-2012291.
文摘In this article,we propose a new finite element spaceΛh for the expanded mixed finite element method(EMFEM)for second-order elliptic problems to guarantee its computing capability and reduce the computation cost.The new finite element spaceΛh is designed in such a way that the strong requirement V h⊂Λh in[9]is weakened to{v h∈V h;d i v v h=0}⊂Λh so that it needs fewer degrees of freedom than its classical counterpart.Furthermore,the newΛh coupled with the Raviart-Thomas space satisfies the inf-sup condition,which is crucial to the computation of mixed methods for its close relation to the behavior of the smallest nonzero eigenvalue of the stiff matrix,and thus the existence,uniqueness and optimal approximate capability of the EMFEM solution are proved for rectangular partitions in R d,d=2,3 and for triangular partitions in R 2.Also,the solvability of the EMFEM for triangular partition in R 3 can be directly proved without the inf-sup condition.Numerical experiments are conducted to confirm these theoretical findings.
基金Supported by the National Natural Science Foundation of China(11271127)Science Research Projectof Guizhou Province Education Department(QJHKYZ[2013]207)
文摘A reduced-order extrapolation algorithm based on Crank-Nicolson least-squares mixed finite element （CNLSMFE） formulation and proper orthogonal decomposition （POD） technique for two-dimensional （2D） Sobolev equations is established. The error estimates of the reduced-order CNLSMFE solutions and the implementation for the reduced-order extrapolation algorithm are provided. A numerical example is used to show that the results of numerical computations are consistent with theoretical conclusions. Moreover, it is shown that the reduced-order extrapolation algorithm is feasible and efficient for seeking numerical solutions to 2D Sobolev equations.
