Fully computable a posteriori error bounds for eigenfunctions

Fully computable a posteriori error estimates for eigenfunctions of compact self-adjoint operators in Hilbert spaces are derived. The problem of ill-conditioning of eigenfunctions in case of tight clusters and multiple eigenvalues is solved by estimating the directed distance between the spaces of exact and approximate eigenfunctions. Derived upper bounds apply to various types of eigenvalue problems, e.g. to the (generalized) matrix, Laplace, and Steklov eigenvalue problems. These bounds are suitable for arbitrary conforming approximations of eigenfunctions, and they are fully computable in terms of approximate eigenfunctions and two-sided bounds of eigenvalues. Numerical examples illustrate the efficiency of the derived error bounds for eigenfunctions.Comment: 27 pages, 8 tables, 9 figure

Explicit estimation of error constants appearing in non-conforming linear triangular finite element method

summary:The non-conforming linear ($P_1$) triangular FEM can be viewed as a kind of the discontinuous Galerkin method, and is attractive in both the theoretical and practical purposes. Since various error constants must be quantitatively evaluated for its accurate a priori and a posteriori error estimates, we derive their theoretical upper bounds and some computational results. In particular, the Babuška-Aziz maximum angle condition is required just as in the case of the conforming $P_1$ triangle. Some applications and numerical results are also included to see the validity and effectiveness of our analysis

Projection error-based guaranteed L2 error bounds for finite element approximations of Laplace eigenfunctions

For conforming finite element approximations of the Laplacian eigenfunctions, a fully computable guaranteed error bound in the $L^2$ norm sense is proposed. The bound is based on the a priori error estimate for the Galerkin projection of the conforming finite element method, and has an optimal speed of convergence for the eigenfunctions with the worst regularity. The resulting error estimate bounds the distance of spaces of exact and approximate eigenfunctions and, hence, is robust even in the case of multiple and tightly clustered eigenvalues. The accuracy of the proposed bound is illustrated by numerical examples. The demonstration code is available at https://ganjin.online/xfliu/EigenfunctionEstimation4FEM .Comment: 24 pages, 7 figures, 3 tables. arXiv admin note: text overlap with arXiv:1904.0790

The Effects of Online and Face-to-face Experiential Value Co-creation on Tourists’ Wellbeing

As the rapid and sustained development of the information communication technology (ICT), tourists can be constantly connected with their original environment. ICT has changed the travel experience which may further influence their satisfactions and wellbeing. The aim of this study is to investigate the impact of online and face-to-face experiential value co-creation on the wellbeing of tourists by using a mixed-methods approach. After introducing scales developed by interviews into a PLS-SEM model, this study reveals that both online and faceto-face experiential value co-creation has positive impact on satisfaction and wellbeing. The trade-off between the two types of co-creations is not significant