5 papers
Weak discrete maximum principle of finite element methods in convex polyhedra
Dmitriy Leykekhman, Buyang Li
We prove that the Galerkin finite element solution of the Laplace equation in a convex polyhedron , with a quasi-uniform tetrahedral partition of the domain and wi…
Global and local pointwise error estimates for finite element approximations to the Stokes problem on convex polyhedra
Niklas Behringer, Dmitriy Leykekhman, Boris Vexler
The main goal of the paper is to show new stability and localization results for the finite element solution of the Stokes system in and norms under sta…
Numerical Analysis of Sparse Initial Data Identification for Parabolic Problems
Dmitriy Leykekhman, Boris Vexler, Daniel Walter
In this paper we consider a problem of initial data identification from the final time observation for homogeneous parabolic problems. It is well-known that such problems are expon…
On the dimension spectrum of infinite subsystems of continued fractions
Vasileios Chousionis, Dmitriy Leykekhman, Mariusz Urbański
In this paper we study the dimension spectrum of continued fractions with coefficients restricted to infinite subsets of natural numbers. We prove that if is any arithmetic pro…
The dimension spectrum of graph directed Markov systems
Vasileios Chousionis, Dmitriy Leykekhman, Mariusz Urbański
In this paper we study the dimension spectrum of general conformal graph directed Markov systems modeled by countable state symbolic subshifts of finite type. We perform a comprehe…