Two basic hypothesises of Taylor-Galerkin Finite Element Method are studied in this paper. One of them which is unreasonable is redefined. The only hypothesis becomes the standpoint of Generalized Finite Element. We u...Two basic hypothesises of Taylor-Galerkin Finite Element Method are studied in this paper. One of them which is unreasonable is redefined. The only hypothesis becomes the standpoint of Generalized Finite Element. We use this idea to analysis stream function-vorticity equations with Modified Taylor-Galerkin Finite Element Method, and give the two-step solving method, which makes the solving process more reasonable than ever before. Several computational examples reveal that the results of this new method are satisfied.展开更多
Residual based on a posteriori error estimates for conforming finite element solutions of incompressible Navier-Stokes equations with stream function form which were computed with seven recently proposed two-level met...Residual based on a posteriori error estimates for conforming finite element solutions of incompressible Navier-Stokes equations with stream function form which were computed with seven recently proposed two-level method were derived. The posteriori error estimates contained additional terms in comparison to the error estimates for the solution obtained by the standard finite element method. The importance of these additional terms in the error estimates was investigated by studying their asymptotic behavior. For optimal scaled meshes, these bounds are not of higher order than of convergence of discrete solution.展开更多
Various mixed formulations of the finite element method (FEM) yield matrix equations involving zero diagonal entries. They are then dealt with by a penaltymethod so that they become non-zero but near zero terms. Howev...Various mixed formulations of the finite element method (FEM) yield matrix equations involving zero diagonal entries. They are then dealt with by a penaltymethod so that they become non-zero but near zero terms. However, the penalty has tobe chosen properly. If it is too large, the matrix equation may become ill-conditioned. Onthe other hand, the matrix equation may give incorrect answer if the penalty is too small.In non-linear regime, the difficulty is more serious because the magnitude order of the matrix varies considerably in the entire loading history. The paper suggests an iteration solution and applies it to non-linear FEM of rubber-like hyper-elasticity. This type of analysisis highly non-linear both in physics and in geometry as well as the strong constraint of incompressibility. The iteration solution is demonstrated to possess super precision and excellent convergence characteristics.展开更多
文摘Two basic hypothesises of Taylor-Galerkin Finite Element Method are studied in this paper. One of them which is unreasonable is redefined. The only hypothesis becomes the standpoint of Generalized Finite Element. We use this idea to analysis stream function-vorticity equations with Modified Taylor-Galerkin Finite Element Method, and give the two-step solving method, which makes the solving process more reasonable than ever before. Several computational examples reveal that the results of this new method are satisfied.
文摘Residual based on a posteriori error estimates for conforming finite element solutions of incompressible Navier-Stokes equations with stream function form which were computed with seven recently proposed two-level method were derived. The posteriori error estimates contained additional terms in comparison to the error estimates for the solution obtained by the standard finite element method. The importance of these additional terms in the error estimates was investigated by studying their asymptotic behavior. For optimal scaled meshes, these bounds are not of higher order than of convergence of discrete solution.
文摘Various mixed formulations of the finite element method (FEM) yield matrix equations involving zero diagonal entries. They are then dealt with by a penaltymethod so that they become non-zero but near zero terms. However, the penalty has tobe chosen properly. If it is too large, the matrix equation may become ill-conditioned. Onthe other hand, the matrix equation may give incorrect answer if the penalty is too small.In non-linear regime, the difficulty is more serious because the magnitude order of the matrix varies considerably in the entire loading history. The paper suggests an iteration solution and applies it to non-linear FEM of rubber-like hyper-elasticity. This type of analysisis highly non-linear both in physics and in geometry as well as the strong constraint of incompressibility. The iteration solution is demonstrated to possess super precision and excellent convergence characteristics.
