14 citations · 25 across the 3 of their papers we have counts for
8 papers
The first eigenvalue and eigenfunction of a nonlinear elliptic system
Farid Bozorgnia, Seyyed Abbas Mohammadi, Tomas Vejchodsky
In this paper, we study the first eigenvalue of a nonlinear elliptic system involving -Laplacian as the differential operator. The principal eigenvalue of the system and the cor…
Fully computable a posteriori error bounds for eigenfunctions
Xuefeng Liu, Tomáš Vejchodský
For compact self-adjoint operators in Hilbert spaces, two algorithms are proposed to provide fully computable a posteriori error estimate for eigenfunction approximation. Both algo…
A Simple Approach to Reliable and Robust A Posteriori Error Estimation for Singularly Perturbed Problems
Mark Ainsworth, Tomas Vejchodsky
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 approxima…
Flux reconstructions in the Lehmann-Goerisch method for lower bounds on eigenvalues
Tomas Vejchodsky
The standard application of the Lehmann-Goerisch method for lower bounds on eigenvalues of symmetric elliptic second-order partial differential operators relies on determination of…
Test Models for Statistical Inference: Two-Dimensional Reaction Systems Displaying Limit Cycle Bifurcations and Bistability
Tomislav Plesa, Tomas Vejchodsky, Radek Erban
Theoretical results regarding two-dimensional ordinary-differential equations (ODEs) with second-degree polynomial right-hand sides are summarized, with an emphasis on limit cycles…
Three methods for two-sided bounds of eigenvalues - a comparison
Tomas Vejchodsky
We compare three finite element based methods designed for two-sided bounds of eigenvalues of symmetric elliptic second order operators. The first method is known as the Lehmann-Go…