Dmitriy Leykekhman and Boris Vexler,
Discrete maximal parabolic regularity for Galerkin finite element methods for non-autonomous parabolic problems, accepted, arXiv:1707.09163.
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
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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.
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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.
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Dmitriy Leykekhman and Boris Vexler,
Finite Element Pointwise Results on Convex Polyhedral Domains, SIAM J. Numer. Anal. 54, No. 2 (2016), pp. 561--587.
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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.
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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.
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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.
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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
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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.
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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.
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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 .
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Dmitriy Leykekhman,
Uniform error estimates in the finite element methods for a singularly perturbed reaction-diffusion problem, Math. Comp. 77 (2008), 21-38.
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Dmitriy Leykekhman,
Pointwise localized error estimates for parabolic finite element equations, Numer. Math. 96 (2004), 583-600.
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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