Dr Alex Bespalov BSc PhD

Alex Bespalov

School of Mathematics
Associate Professor in Numerical Analysis

Contact details

School of Mathematics
Watson Building
University of Birmingham
B15 2TT

Dr Alex Bespalov is Associate Professor in Numerical Analysis and a member of the Applied Mathematics group in the School of Mathematics. Alex 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. Alex's research has been supported by EPSRC and The Alan Turing Institute.

Personal webpage


  • PhD in Computational Mathematics, Russian Academy of Sciences, 1999
  • BSc in Mathematics, 1994


Alex obtained his PhD in Computational Mathematics from the Russian Academy of Sciences in 1999.

Before joining the University of Birmingham, Alex held postdoctoral research positions at Universidad de Concepción (Chile), Brunel University, and the University of Manchester.


Semester 1

LM Topics in Applied Mathematics

Semester 2

LH/LM Numerical Methods and Numerical Linear Algebra

Postgraduate supervision

Alex is happy to discuss potential supervision of PhD research projects in Numerical Analysis with motivated and suitably qualified candidates. Some example projects include those given below.

PhD opportunities


Research Themes

  • 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
  • Software development

Research Activity

Alex specialises in Numerical Analysis. As a mathematician, he is interested to see how intrinsic properties of mathematical models (e.g., differential equations) influence their numerical approximations. He uses these insights together with advanced methods of applied analysis to provide mathematical justification of robust and accurate numerical algorithms tailored to specific problems of practical interest.

One direction of Alex's research concerns numerical methods for problems with uncertain (or, random) inputs. Here, the focus is on the development and analysis of efficient, accurate and practical numerical methods for solving high-dimensional parameter-dependent partial differential equations (PDEs). This research is within a rapidly evolving area of uncertainty quantification, which is at the forefront of modern computational science.

Alex's research in numerical methods for uncertainty quantification goes hand in hand with his expertise in and passion for high-order polynomial approximations. He also studies these in the context of finite element and boundary element methods for deterministic PDE problems posed over non-smooth (not necessarily bounded) domains. Here, non-smoothness of physical domain is one of the key points when thinking of practical applications, e.g., in civil engineering (crack detection) and electromagnetics (radar design).

Alex has been collaborating with many colleagues across the world, notably with Professor Norbert Heuer (Pontificia Universidad Católica de Chile), Professor Ralf Hiptmair (ETH Zurich, Switzerland), Professor Serge Nicaise (Université de Valenciennes, France), Professor Dirk Praetorius (Technical University of Vienna), and Professor David Silvester (University of Manchester).

Other activities

  • Reviewer for Mathematical Reviews (2008-2013)
  • SIAM member (since 2018)


Recent publications


Bespalov, A, Silvester, DJ & Xu, F 2022, 'Error estimation and adaptivity for stochastic collocation finite elements. Part I: single-level approximation', SIAM Journal on Scientific Computing.

Bespalov, A, Praetorius, D & Ruggeri, M 2021, 'Convergence and rate optimality of adaptive multilevel stochastic Galerkin FEM', I M A Journal of Numerical Analysis. https://doi.org/10.1093/imanum/drab036

Bespalov, A, Loghin, D & Youngnoi, R 2021, 'Truncation preconditioners for Stochastic Galerkin finite element discretizations', SIAM Journal on Scientific Computing, vol. 2021, pp. S92-S116. https://doi.org/10.1137/20M1345645

Bespalov, A, Praetorius, D & Ruggeri, M 2021, 'Two-level a posteriori error estimation for adaptive multilevel stochastic Galerkin Finite Element Method', SIAM/ASA Journal on Uncertainty Quantification, vol. 9, no. 3, pp. 1184-1216. https://doi.org/10.1137/20M1342586

Bespalov, A & Xu, F 2020, 'A posteriori error estimation and adaptivity in stochastic Galerkin FEM for parametric elliptic PDEs: beyond the affine case', Computers & Mathematics with Applications, vol. 80, no. 5. <https://arxiv.org/pdf/1903.06520>

Khan, A, Bespalov, A, Powell, C & Silvester, D 2020, 'Robust a posteriori error estimation for stochastic Galerkin formulations of parameter dependent linear elasticity equations', Mathematics of Computation, vol. 0, 3572. https://doi.org/10.1090/mcom/3572

Bespalov, A, Rocchi, L & Silvester, D 2020, 'T-IFISS: a toolbox for adaptive FEM computation', Computers & Mathematics with Applications. https://doi.org/10.1016/j.camwa.2020.03.005

Bespalov, A, Betcke, T, Haberl, A & Praetorius, D 2019, 'Adaptive BEM with optimal convergence rates for the Helmholtz equation', Computer Methods in Applied Mechanics and Engineering, vol. 346, pp. 260-287. https://doi.org/10.1016/j.cma.2018.12.006

Bespalov, A, Praetorius, D, Rocchi, L & Ruggeri, M 2019, 'Convergence of adaptive stochastic Galerkin FEM', SIAM Journal on Numerical Analysis, vol. 57, no. 5, pp. 2359–2382. https://doi.org/10.1137/18M1229560

Crowder, A, Powell, C & Bespalov, A 2019, 'Efficient adaptive multilevel stochastic Galerkin approximation using implicit a posteriori error estimation', SIAM Journal on Scientific Computing, vol. 41, no. 3, pp. A1681-A1705. https://doi.org/10.1137/18M1194420

Bespalov, A & Rocchi, L 2018, 'Efficient adaptive algorithms for elliptic PDEs with random data', SIAM/ASA Journal on Uncertainty Quantification, vol. 6, no. 1, pp. 243–272 . https://doi.org/10.1137/17M1139928

Bespalov, A, Praetorius, D, Rocchi, L & Ruggeri, M 2018, 'Goal-oriented error estimation and adaptivity for elliptic PDEs with parametric or uncertain inputs', Computer Methods in Applied Mechanics and Engineering. https://doi.org/10.1016/j.cma.2018.10.041

Bespalov, A, Haberl, A & Praetorius, D 2017, 'Adaptive FEM with coarse initial mesh guarantees optimal convergence rates for compactly perturbed elliptic problems', Computer Methods in Applied Mechanics and Engineering, vol. 317, pp. 318-340. https://doi.org/10.1016/j.cma.2016.12.014

Bespalov, A & Nicaise, S 2016, 'A priori error analysis of the BEM with graded meshes for the electric field integral equation on polyhedral surfaces', Computers & Mathematics with Applications, vol. 71, no. 8, pp. 1636-1644. https://doi.org/10.1016/j.camwa.2016.03.013

Bespalov, A & Silvester, D 2016, 'Efficient adaptive stochastic Galerkin methods for parametric operator equations', SIAM Journal on Scientific Computing, vol. 38, no. 4, pp. A2118–A2140. https://doi.org/10.1137/15M1027048

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