D. Leykekhman and B. Li,
Weak discrete maximum principle of
finite element methods in convex polyhedra, submitted, arXiv:1909.06783.
Preprint
D. Leykekhman,
Pointwise error estimates for $C^0$ interior penalty approximation of biharmonic problems, submitted.
Preprint
N. Behringer, D. Leykekhman, B. Vexler,
Global and local pointwise error estimates for finite element approximations to the Stokes problem on convex polyhedra, submitted, arXiv:1907.06871.
Preprint
D. Leykekhman, B. Vexler, and D. Walter
Numerical Analysis of Sparse Initial Data Identification for Parabolic Problems, submitted, arXiv:1905.01226.
Preprint
V. Chousionis, D. Leykekhman, and M. Urbanski,
On the dimension spectrum of infinite subsystems of continued fractions, accepted to Transactions of the American Mathematical Society, arXiv:1805.11904 .
Preprint
V. Chousionis, D. Leykekhman, and M. Urbanski,
The dimension spectrum of graph directed Markov systems, Sel. Math. New Ser. (2019) 25:40.
Preprint
Dmitriy Leykekhman and Boris Vexler,
Discrete maximal parabolic regularity for Galerkin finite element methods for non-autonomous parabolic problems, SIAM J. Numer. Anal. 56, No. 4 (2018), pp. 2178--2202.
Preprint
Harbir Antil and Dmitriy Leykekhman,
A brief introduction to PDE-constrained optimii
zation. Frontiers in PDE-constrained optimization, IMA Vol. Math. Appl. 163, (2018), pp. 3--40.
Preprint
Dmitriy Leykekhman and Boris Vexler,
Optimal a priori error estimates of parabolic optimal control problems with a moving point control, Solvability, regularity, and optimal control of boundary value problems for PDEs, 327--356,
Springer INdAM Ser., 22, Springer, Cham, 2017.
Preprint
Dmitriy Leykekhman and Boris Vexler,
Global and interior pointwise best approximation results for the gradient of Galerkin solutions for parabolic problem, SIAM J. Numer. Anal. 55, No. 4 (2017), pp. 2025--2049.
Preprint
Dmitriy Leykekhman and Buyang Li,
Maximum-norm stability of the finite element
Ritz projection with mixed boundary conditions, Calcolo 54 (2017) no. 2, 541--565.
Preprint
Dmitriy Leykekhman and Boris Vexler,
Discrete maximal parabolic regularity for Galerkin finite element methods, Numer. Math., 135 (2017), no. 3, 923--952.
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Dmitriy Leykekhman and Michael Pruitt,
On the Positivity of Discrete Harmonic Functions and the Discrete Harnack Inequality for Piecewise Linear Finite Elements, Math. Comp. 86 (2017), 1127--1145
Preprint
Dmitriy Leykekhman and Boris Vexler,
A priori error estimates for three dimensional parabolic optimal control problems with pointwise control, SIAM J. Control Optim., 54 No. 5 (2016), pp. 2403--2435.
Preprint
Dmitriy Leykekhman and Boris Vexler,
Pointwise best approximation results for Galerkin finite element solutions of parabolic problems, SIAM J. Numer. Anal. 54, No. 3 (2016), pp. 1365--1384.
Preprint
Dmitriy Leykekhman and Boris Vexler,
Finite Element Pointwise Results on Convex Polyhedral Domains, SIAM J. Numer. Anal. 54, No. 2 (2016), pp. 561--587.
Preprint
Dmitriy Leykekhman, Dominik Meidner, and Boris Vexler,
Optimal error estimates for finite element discretization of
elliptic optimal control problems with finitely many pointwise
state constraints, Computational Optimization and Applications, 55, No. 3 (2013), 769--802.
Preprint
Dmitriy Leykekhman and Boris Vexler,
Optimal a priori error estimates of parabolic optimal control problems with pointwise control, SIAM J. Numer. Anal., 51, no. 5 (2013), 2797--2821.
Preprint
Dmitriy Leykekhman and Matthias Heinkenschloss,
Local error analysis of discontinuous Galerkin methods for advection-dominated elliptic
linear-quadratic optimal control problems, SIAM J. Numer. Anal. 50, no. 4 (2012), 2012-2038.
Preprint
Dmitriy Leykekhman,
Investigation of Commutative Properties of Discontinuous
Galerkin Methods in PDE Constrained Optimal Control
Problems,
Journal of Scientific Computing. Volume 53, Number 3 (2012), 483-511.
DOI: 10.1007/s10915-012-9582-y
Preprint
Johnny Guzman, Dmitriy Leykekhman, and Michael Neilan,
A family of non-conforming elements and the analysis of Nitsche’s method for a
singularly perturbed fourth order problem,
Calcolo, Volume 49, Number 2 (2012), 95-125.
DOI: 10.1007/s10092-011-0047-8
Preprint
Johnny Guzman and Dmitriy Leykekhman,
Pointwise error estimates of finite element approximations to the Stokes problem on convex polyhedra,
Math. Comp. 81 (2012), 1879-1902
DOI: 10.1090/S0025-5718-2012-02603-2
Preprint
Alan Demlow, Dmitriy Leykekhman, Alfred .H. Schatz, and Lars B. Wahlbin,
Best approximation property in the $W_\infty^1$ norm on graded meshes, Math. Comp. 81 (2012), 743-764
Preprint
Matthias Heinkenschloss and Dmitriy Leykekhman,
Local error estimates for SUPG solutions of
advection-dominated elliptic linear-quadratic optimal control problems, SIAM J. Numer. Anal. 47, no. 6 (2010), 4607-4638.
Preprint
Johnny Guzman, Dmitriy Leykekhman, Jurgen Rossmann, and Alfred H. Schatz,
Optimal max-norm error estimates for the finite element
method and Holder estimates for the Green's function on convex
polyhedral domains, Numer. Math.,
112 (2009), no. 2, 221-243.
Preprint
Eris Burman, Johnny Guzman, and Dmitriy Leykekhman,
Weighted a priori error estimates for continuous interior penalty method, IMA J. Numer. Math. 29 (2009), no. 2, 284-314.
Preprint
Dmitriy Leykekhman and Lars B. Wahlbin,
A posteriori error estimate by
recovered gradients in the parabolic finite element equation, BIT Numerical Mathematics, Volume 48, Number 3 (2008), 585-605 .
Preprint
Dmitriy Leykekhman,
Uniform error estimates in the finite element methods for a singularly perturbed reaction-diffusion problem, Math. Comp. 77 (2008), 21-38.
Preprint
Dmitriy Leykekhman,
Pointwise localized error estimates for parabolic finite element equations, Numer. Math. 96 (2004), 583-600.
Preprint
Dmitriy Leykekhman and Matthias Heinkenschloss,
Local Error Analysis of Discontinuous
Galerkin Methods for Advection-Dominated Elliptic Linear-Quadratic Optimal Control Problems, Tech. Report TR10–
11, Department of Computational and Applied Mathematics, Rice University, Houston, TX
77005–1892, 2008.
Preprint
Matthias Heinkenschloss and Dmitriy Leykekhman,
Local error estimates for SUPG solutions of
advection-dominated elliptic linear-quadratic optimal control problems, Tech. Report TR08–
30, Department of Computational and Applied Mathematics, Rice University, Houston, TX
77005–1892, 2008.
Preprint