Zobrazeno 1 - 10
of 160
pro vyhledávání: '"VEJCHODSKÝ, TOMÁŠ"'
Autor:
Liu, Xuefeng, Vejchodský, Tomáš
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 conformi
Externí odkaz:
http://arxiv.org/abs/2211.03218
In this paper, we study the first eigenvalue of a nonlinear elliptic system involving $p$-Laplacian as the differential operator. The principal eigenvalue of the system and the corresponding eigenfunction are investigated both analytically and numeri
Externí odkaz:
http://arxiv.org/abs/1905.12059
Autor:
Dolgov, Sergey, Vejchodský, Tomáš
We propose a guaranteed and fully computable upper bound on the energy norm of the error in low-rank Tensor Train (TT) approximate solutions of (possibly) high dimensional reaction-diffusion problems. The error bound is obtained from Euler-Lagrange e
Externí odkaz:
http://arxiv.org/abs/1905.08572
Autor:
Liu, Xuefeng, Vejchodský, Tomáš
Publikováno v:
Numerische Mathematik (2022)
For compact self-adjoint operators in Hilbert spaces, two algorithms are proposed to provide fully computable a posteriori error estimate for eigenfunction approximation. Both algorithms apply well to the case of tight clusters and multiple eigenvalu
Externí odkaz:
http://arxiv.org/abs/1904.07903
Autor:
Ainsworth, Mark, Vejchodsky, Tomas
A simple flux reconstruction for finite element solutions of reaction-diffusion problems is shown to yield fully computable upper bounds on the energy norm of error in an approximation of singularly perturbed reaction-diffusion problem. The flux reco
Externí odkaz:
http://arxiv.org/abs/1812.07972