Submitted papers:
Published and accepted papers:
Fully discrete best approximation type estimates in $L^\infty(I;L^2(\Omega)^d)$ for finite element discretizations of the transient Stokes equations,
accepted to IMA J. Numerical Analysis, arXiv:2107.11051.
Preprint
Local energy estimates for the fractional Laplacian,
SIAM J. Numer. Anal. 59 (2021), 1918--1947.
Preprint
Pointwise error estimates for $C^0$ interior penalty approximation of biharmonic problems,
Math. Comp. 90 (2021), 41--63.
Preprint
Weak discrete maximum principle of finite element methods in convex polyhedra,
Math. Comp. 90 (2021), 1--18.
Preprint
Global and local pointwise error estimates for finite element approximations to the Stokes problem on convex polyhedra,
SIAM J. Numer. Anal. 58 (2020), no. 3, 1531--1555.
Preprint
Numerical Analysis of Sparse Initial Data Identification for Parabolic Problems,
ESAIM: M2AN 54 (2020) 1139--1180, arXiv:1905.01226.
Preprint
On the dimension spectrum of infinite subsystems of continued fractions,
Trans. Amer. Math. Soc. 373 (2020), no. 2, 1009--1042, arXiv:1805.11904 .
Preprint
The dimension spectrum of graph directed Markov systems,
Sel. Math. New Ser. (2019) 25:40.
Preprint
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
A brief introduction to PDE-constrained optimii zation. Frontiers in PDE-constrained optimization,
IMA Vol. Math. Appl. 163, (2018), pp. 3--40.
Preprint
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
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
Maximum-norm stability of the finite element Ritz projection with mixed boundary conditions,
Calcolo 54 (2017) no. 2, 541--565.
Preprint
Discrete maximal parabolic regularity for Galerkin finite element methods,
Numer. Math., 135 (2017), no. 3, 923--952.
Preprint
On the Positivity of Discrete Harmonic Functions and the Discrete Harnack Inequality for Piecewise Linear Finite Elements,
Math. Comp. 86 (2017), 1127--1145
Preprint
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
Pointwise best approximation results for Galerkin finite element solutions of parabolic problems,
SIAM J. Numer. Anal. 54, No. 3 (2016), pp. 1365--1384.
Preprint
Finite Element Pointwise Results on Convex Polyhedral Domains,
SIAM J. Numer. Anal. 54, No. 2 (2016), pp. 561--587.
Preprint
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
Optimal a priori error estimates of parabolic optimal control problems with pointwise control,
SIAM J. Numer. Anal., 51, no. 5 (2013), 2797--2821.
Preprint
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
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
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
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
Best approximation property in the $W_\infty^1$ norm on graded meshes,
Math. Comp. 81 (2012), 743-764
Preprint
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
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
Weighted a priori error estimates for continuous interior penalty method,
IMA J. Numer. Math. 29 (2009), no. 2, 284-314.
Preprint
A posteriori error estimate by recovered gradients in the parabolic finite element equation,
BIT Numerical Mathematics, Volume 48, Number 3 (2008), 585-605 .
Preprint
Uniform error estimates in the finite element methods for a singularly perturbed reaction-diffusion problem,
Math. Comp. 77 (2008), 21-38.
Preprint
Pointwise localized error estimates for parabolic finite element equations,
Numer. Math. 96 (2004), 583-600.
Preprint