6 papers · 1 filter
Guaranteed Lower Eigenvalue Bounds for Spectral Galerkin Methods with Application to Schrödinger Operators
Xuefeng Liu
Spectral Galerkin methods are renowned for high-precision eigenvalue approximation, yet a rigorous lower bound obtained directly from a spectral discretisation has remained unavail…
Explicit Two-Sided Eigenvalue Bounds for Schrödinger Operators with Singular Potentials via Finite Element Method
Xuefeng Liu
We present, to the best of our knowledge, the first numerical algorithm for explicit, computable two-sided eigenvalue bounds for Schrödinger operators H = -Delta + V on R^N, N = 2,…
Rigorous Eigenvalue Bounds for Schrödinger Operators with Confining Potentials on
Xuefeng Liu
We propose a rigorous method for computing two-sided eigenvalue bounds of the Schrödinger operator with a confining potential on . The method combines domain…
Projection error-based guaranteed L2 error bounds for finite element approximations of Laplace eigenfunctions
Xuefeng Liu, Tomáš Vejchodský
For conforming finite element approximations of the Laplacian eigenfunctions, a fully computable guaranteed error bound in the norm sense is proposed. The bound is based on t…
Shape optimization for the Laplacian eigenvalue over triangles and its application to interpolation error constant estimation
Ryoki Endo, Xuefeng Liu
A computer-assisted proof is proposed for the Laplacian eigenvalue minimization problems over triangular domains under diameter constraints. The proof utilizes recently developed g…
Explicit a posteriori and a priori error estimation for the finite element solution of Stokes equations
Xuefeng Liu, Mitsuhiro Nakao, Chun'guang You +1
For the Stokes equation over 2D and 3D domains, explicit a posteriori and a priori error estimation are novelly developed for the finite element solution. The difficulty in handlin…