Based on flux-based formulation, a nodeless variable element method is developed to analyze two-dimensional steady-state and transient heat transfer problems. The nodeless variable element employs quadratic interpolat...Based on flux-based formulation, a nodeless variable element method is developed to analyze two-dimensional steady-state and transient heat transfer problems. The nodeless variable element employs quadratic interpolation functions to provide higher solution accuracy without necessity to actually generate additional nodes. The flux-based formulation is applied to reduce the complexity in deriving the finite element equations as compared to the conventional finite element method, The solution accuracy is further improved by implementing an adaptive meshing technique to generaie finite element mesh that can adapt and move along corresponding to the solution behavior. The technique generates small elements in the regions of steep solution gradients to provide accurate solution, and meanwhile it generates larger elements in the other regions where the solution gradients are slight to reduce the computational time and the computer memory. The effectiveness of the combined procedure is demonstrated by heat transfer problems that have exact solutions. These problems tire： （a） a steady-state heat conduction analysis in a square plate subjected to a highly localized surface heating, and （b） a transient heat conduction analysis in a long plate subjected to moving heat source.展开更多
We present quantitative studies of transfer operators between finite element spaces associated with unrelated meshes.Several local approximations of the global L^(2)-orthogonal projection are reviewed and evaluated co...We present quantitative studies of transfer operators between finite element spaces associated with unrelated meshes.Several local approximations of the global L^(2)-orthogonal projection are reviewed and evaluated computationally.The numerical studies in 3D provide the first estimates of the quantitative differences between a range of transfer operators between non-nested finite element spaces.We consider the standard finite element interpolation,Cl´ement’s quasi-interpolation with different local polynomial degrees,the global L^(2)-orthogonal projection,a local L^(2)-quasi-projection via a discrete inner product,and a pseudo-L^(2)-projection defined by a Petrov-Galerkin variational equation with a discontinuous test space.Understanding their qualitative and quantitative behaviors in this computational way is interesting per se;it could also be relevant in the context of discretization and solution techniques which make use of different non-nested meshes.It turns out that the pseudo-L^(2)-projection approximates the actual L^(2)-orthogonal projection best.The obtained results seem to be largely independent of the underlying computational domain;this is demonstrated by four examples(ball,cylinder,half torus and Stanford Bunny).展开更多
文摘Based on flux-based formulation, a nodeless variable element method is developed to analyze two-dimensional steady-state and transient heat transfer problems. The nodeless variable element employs quadratic interpolation functions to provide higher solution accuracy without necessity to actually generate additional nodes. The flux-based formulation is applied to reduce the complexity in deriving the finite element equations as compared to the conventional finite element method, The solution accuracy is further improved by implementing an adaptive meshing technique to generaie finite element mesh that can adapt and move along corresponding to the solution behavior. The technique generates small elements in the regions of steep solution gradients to provide accurate solution, and meanwhile it generates larger elements in the other regions where the solution gradients are slight to reduce the computational time and the computer memory. The effectiveness of the combined procedure is demonstrated by heat transfer problems that have exact solutions. These problems tire： （a） a steady-state heat conduction analysis in a square plate subjected to a highly localized surface heating, and （b） a transient heat conduction analysis in a long plate subjected to moving heat source.
基金supported by the Bonn International Graduate School in Mathematics and by the Iniziativa Ticino in Rete.
文摘We present quantitative studies of transfer operators between finite element spaces associated with unrelated meshes.Several local approximations of the global L^(2)-orthogonal projection are reviewed and evaluated computationally.The numerical studies in 3D provide the first estimates of the quantitative differences between a range of transfer operators between non-nested finite element spaces.We consider the standard finite element interpolation,Cl´ement’s quasi-interpolation with different local polynomial degrees,the global L^(2)-orthogonal projection,a local L^(2)-quasi-projection via a discrete inner product,and a pseudo-L^(2)-projection defined by a Petrov-Galerkin variational equation with a discontinuous test space.Understanding their qualitative and quantitative behaviors in this computational way is interesting per se;it could also be relevant in the context of discretization and solution techniques which make use of different non-nested meshes.It turns out that the pseudo-L^(2)-projection approximates the actual L^(2)-orthogonal projection best.The obtained results seem to be largely independent of the underlying computational domain;this is demonstrated by four examples(ball,cylinder,half torus and Stanford Bunny).
