Alex Bespalov

Accepting PhD Students

PhD projects

Alex Bespalov is a numerical analyst with expertise in a range of modern computational methods and techniques. His research aims at the design, analysis and implementation of robust and accurate numerical algorithms for solving mathematical problems coming from real-life applications. His research interests include:

numerical solution of partial differential and boundary integral equations;
numerical methods for uncertainty quantification;
high order (p- and hp-) finite element and boundary element methods;
error estimation, error control, and adaptivity;
singularities and their numerical approximation;
applications to electromagnetics, linear elasticity, and fluid dynamics
Dr Bespalov is happy to discuss potential supervision of PhD research projects in Numerical Analysis with motivated and suitably qualified candidates.

Research activity per year

23 Article

23 results

2023
Error estimation and adaptivity for stochastic collocation finite elements part II: multilevel approximation
Bespalov, A. & Silvester, DJ., 27 Apr 2023, In: SIAM Journal on Scientific Computing. 45, 2, p. A781-A797 17 p.
Research output: Contribution to journal › Article › peer-review

Open Access
File
18 Downloads (Pure)
2022
Error estimation and adaptivity for stochastic collocation finite elements. Part I: single-level approximation
Bespalov, A., Silvester, DJ. & Xu, F., Oct 2022, In: SIAM Journal on Scientific Computing. 44, 5, p. A3393-A3412 20 p.
Research output: Contribution to journal › Article › peer-review

Open Access
File
20 Downloads (Pure)
2021
Convergence and rate optimality of adaptive multilevel stochastic Galerkin FEM
Bespalov, A., Praetorius, D. & Ruggeri, M., 19 May 2021, (E-pub ahead of print) In: I M A Journal of Numerical Analysis.
Research output: Contribution to journal › Article › peer-review

Open Access
File
28 Downloads (Pure)
Truncation preconditioners for Stochastic Galerkin finite element discretizations
Bespalov, A., Loghin, D. & Youngnoi, R., 15 Mar 2021, (E-pub ahead of print) In: SIAM Journal on Scientific Computing. 2021, p. S92-S116
Research output: Contribution to journal › Article › peer-review

Open Access
File
176 Downloads (Pure)
Two-level a posteriori error estimation for adaptive multilevel stochastic Galerkin Finite Element Method
Bespalov, A., Praetorius, D. & Ruggeri, M., 16 Sept 2021, In: SIAM/ASA Journal on Uncertainty Quantification. 9, 3, p. 1184-1216 33 p.
Research output: Contribution to journal › Article › peer-review

Open Access
File
72 Downloads (Pure)
2020
A posteriori error estimation and adaptivity in stochastic Galerkin FEM for parametric elliptic PDEs: beyond the affine case
Bespalov, A. & Xu, F., 30 May 2020, (Accepted/In press) In: Computers & Mathematics with Applications. 80, 5, 20 p.
Research output: Contribution to journal › Article › peer-review

Open Access
Robust a posteriori error estimation for stochastic Galerkin formulations of parameter dependent linear elasticity equations
Khan, A., Bespalov, A., Powell, C. & Silvester, D., 16 Nov 2020, In: Mathematics of Computation. 0, 3572.
Research output: Contribution to journal › Article › peer-review

Open Access
File
175 Downloads (Pure)
T-IFISS: a toolbox for adaptive FEM computation
Bespalov, A., Rocchi, L. & Silvester, D., 27 Mar 2020, (E-pub ahead of print) In: Computers & Mathematics with Applications. 81, p. 373-390
Research output: Contribution to journal › Article › peer-review

Open Access
File
2 Citations (Scopus)

103 Downloads (Pure)
2019
Adaptive BEM with optimal convergence rates for the Helmholtz equation
Bespalov, A., Betcke, T., Haberl, A. & Praetorius, D., 1 Apr 2019, In: Computer Methods in Applied Mechanics and Engineering. 346, p. 260-287 34 p.
Research output: Contribution to journal › Article › peer-review

Open Access
File
7 Citations (Scopus)

93 Downloads (Pure)
Convergence of adaptive stochastic Galerkin FEM
Bespalov, A., Praetorius, D., Rocchi, L. & Ruggeri, M., 3 Oct 2019, In: SIAM Journal on Numerical Analysis. 57, 5, p. 2359–2382 24 p.
Research output: Contribution to journal › Article › peer-review

Open Access
File
2 Citations (Scopus)

209 Downloads (Pure)
Efficient adaptive multilevel stochastic Galerkin approximation using implicit a posteriori error estimation
Crowder, A., Powell, C. & Bespalov, A., 21 May 2019, In: SIAM Journal on Scientific Computing. 41, 3, p. A1681-A1705 25 p.
Research output: Contribution to journal › Article › peer-review

Open Access
File
4 Citations (Scopus)

273 Downloads (Pure)
2018
Efficient adaptive algorithms for elliptic PDEs with random data
Bespalov, A. & Rocchi, L., 2018, In: SIAM/ASA Journal on Uncertainty Quantification. 6, 1, p. 243–272
Research output: Contribution to journal › Article › peer-review

Open Access
File
8 Citations (Scopus)

216 Downloads (Pure)
Goal-oriented error estimation and adaptivity for elliptic PDEs with parametric or uncertain inputs
Bespalov, A., Praetorius, D., Rocchi, L. & Ruggeri, M., 30 Oct 2018, (E-pub ahead of print) In: Computer Methods in Applied Mechanics and Engineering. 39 p.
Research output: Contribution to journal › Article › peer-review

Open Access
File
4 Citations (Scopus)

157 Downloads (Pure)
2017
Adaptive FEM with coarse initial mesh guarantees optimal convergence rates for compactly perturbed elliptic problems
Bespalov, A., Haberl, A. & Praetorius, D., 15 Apr 2017, In: Computer Methods in Applied Mechanics and Engineering. 317, p. 318-340 23 p.
Research output: Contribution to journal › Article › peer-review

Open Access
File
18 Citations (Scopus)

122 Downloads (Pure)
2016
A priori error analysis of the BEM with graded meshes for the electric field integral equation on polyhedral surfaces
Bespalov, A. & Nicaise, S., Apr 2016, In: Computers & Mathematics with Applications. 71, 8, p. 1636-1644 9 p.
Research output: Contribution to journal › Article › peer-review

Open Access
File
132 Downloads (Pure)
Efficient adaptive stochastic Galerkin methods for parametric operator equations
Bespalov, A. & Silvester, D., 7 Jul 2016, In: SIAM Journal on Scientific Computing. 38, 4, p. A2118–A2140 23 p.
Research output: Contribution to journal › Article › peer-review

Open Access
File
15 Citations (Scopus)

208 Downloads (Pure)
2015
The BEM with graded meshes for the electric field integral equation on polyhedral surfaces
Bespalov, A. & Nicaise, S., 21 Jun 2015, In: Numerische Mathematik. 132, 4, 25 p.
Research output: Contribution to journal › Article › peer-review

Open Access
File
1 Citation (Scopus)

129 Downloads (Pure)
2014
Energy norm a posteriori error estimation for parametric operator equations
Bespalov, A., Powell, C. E. & Silvester, DJ., 2014, In: SIAM Journal on Scientific Computing. 36, 2, p. A339-A363 25 p.
Research output: Contribution to journal › Article › peer-review

Open Access
File
30 Citations (Scopus)

132 Downloads (Pure)
2012
A priori error analysis of stochastic galerkin mixed approximations of elliptic pdes with random data
Bespalov, A., Powell, C. E. & Silvester, D., 1 Jan 2012, In: SIAM Journal on Numerical Analysis. 50, 4, p. 2039-2063 25 p.
Research output: Contribution to journal › Article › peer-review
14 Citations (Scopus)
Natural hp-BEM for the electric field integral equation with singular solutions
Bespalov, A. & Heuer, N., 1 Sept 2012, In: Numerical Methods for Partial Differential Equations. 28, 5
Research output: Contribution to journal › Article › peer-review
2010
Convergence of the natural hp-BEM for the electric field integral equation on polyhedral surfaces
Bespalov, A., Heuer, N. & Hiptmair, R., 1 Jan 2010, In: SIAM Journal on Numerical Analysis. 48, 4, p. 1518-1529 12 p.
Research output: Contribution to journal › Article › peer-review
15 Citations (Scopus)
Natural p-BEM for the electric field integral equation on screens
Bespalov, A. & Heuer, N., 1 Jul 2010, In: I M A Journal of Numerical Analysis. 30, 3, p. 595-628 34 p.
Research output: Contribution to journal › Article › peer-review
6 Citations (Scopus)
2009

Optimal Error Estimation for ${\bfH}({\rmcurl})$-Conforming p -Interpolation in Two Dimensions
Bespalov, A. & Heuer, N., 1 Jan 2009, In: SIAM Journal on Numerical Analysis. 47, 5, p. 3977-3989
Research output: Contribution to journal › Article › peer-review

Alex Bespalov

Research output

Search results