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
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).
