My research interests are in the fields of Numerical Analysis and Scientific Computing, in particular:

• Numerical methods for uncertainty quantification in problems with random parameters
• Finite Element Methods, high-order and spectral FEM
• Boundary Element Methods, discretization of nonlocal operators
• Numerical integration
• Numerical methods for high-dimensional problems
• Numerical methods for contact and obstacle problems

Current members

PhD student

Postdoctoral research fellow

Alumni

Postdoctoral research fellows

PhD students

• Lourenço Beirão da Veiga, University of Milano-Bicocca, Italy
• Claudio Bierig, Robert Bosch GmbH, Abstatt, Germany
• Dinh Dũng, Vietnam National University, Hanoi, Vietnam
• Herbert Egger, Universität Linz, Austria
• Frances Y. Kuo, University of New South Wales, Sydney, Australia
• Matthias Maischak, Brunel University, United Kingdom
• Lorenzo Mascotto, University of Milano-Bicocca, Italy
• Duong T. Pham, Vietnamese-German University, Vietnam
• Anne Reinarz, University of Durham, UK
• Alessandro Russo, University of Milano-Bicocca, Italy
• Erik M. Schetzke, Fraunhofer-Institute FKIE, Wachtberg, Germany
• Kersten Schmidt, TU Darmstadt, Germany
• Christoph Schwab, ETH Zurich, Switzerland
• Ian H. Sloan, University of New South Wales, Sydney, Australia
• Ernst P. Stephan, University of Hanover, Germany
• Thanh Tran, University of New South Wales, Sydney, Australia
• Tobias von Petersdorff, University of Maryland, College Park, USA

Preprints

1. A. Chernov and T. Lê, Analytic and Gevrey class regularity for parametric elliptic eigenvalue problems and applications, SIAM J. Numer. Anal. (2024), accepted, Preprint

2. N. Wulbusch, R. Roden, M. Blau and A. Chernov, Bayesian parameter identification in impedance boundary conditions for Helmholtz problems, SIAM J. Sci. Comput (2024), accepted, Preprint

Peer-reviewed Publications

1. A. Chernov and T. Lê, Analytic and Gevrey class regularity for parametric semilinear reaction-diffusion problems and applications in uncertainty quantification, Comput. Math. Appl., 164 (2024), 116–130, DOI: 10.1016/j.camwa.2024.04.007, Preprint

2. A. Chernov and E. M. Schetzke, A simple, bias-free approximation of covariance functions by the multilevel Monte Carlo method having nearly optimal complexity, SIAM/ASA J. Uncertain. Quantif., 11 (2023), no. 3, 941–969, DOI: 10.1137/22M1506845, Preprint

3. N. Wulbusch, R. Roden, A. Chernov and M. Blau, Using a one-dimensional finite-element approximation of Webster's horn equation to estimate individual ear canal acoustic transfer from input impedances, J. Acoust. Soc. Am., 153 (2023), no. 5, 2826–2837, DOI: 10.1121/10.0019378, Preprint

4. A. Chernov, C. Marcati and L. Mascotto, p- and hp-virtual elements for the Stokes problem, Adv. Comput. Math., 47 (2021), no. 2, Paper No. 24, 31 pp., DOI: 10.1007/s10444-020-09831-w, Preprint

5. A. Chernov, H. Hoel, K. Law, F. Nobile and R. Tempone, Multilevel ensemble Kalman filtering for spatio-temporal processes, Numer. Math. 147 (2021), no. 1, 71–125, DOI: 10.1007/s00211-020-01159-3, Preprint

6. F. Schöpfer and A. Chernov, Certified efficient global roundness evaluation, J. Optim. Theory Appl., 186 (2020), no.1, 169–190, DOI: 10.1007/s10957-020-01689-8

7. D. T. Pham, T. Tran, D. Dũng and A. Chernov, Exterior Dirichlet and Neumann problems in domains with random boundaries, Bull. Malays. Math. Sci. Soc., 43 (2020), no. 2, 1311–1342, DOI: 10.1007/s40840-019-00741-9

8. A. Chernov and A. Reinarz, Sparse grid approximation spaces for space-time boundary integral formulations of the heat equation, Comput. Math. Appl., 78 (2019), no. 11, 3605–3619, DOI: 10.1016/j.camwa.2019.06.036, Preprint

9. A. Chernov and L. Mascotto, The harmonic virtual element method: stabilization and exponential convergence for the Laplace problem on polygonal domains, IMA J. Numer. Anal., 39 (2019), no. 4, 1787–1817, DOI: 10.1093/imanum/dry038, Preprint

10. L. Beirão da Veiga, A. Chernov, L. Mascotto and A. Russo, Exponential convergence of the hp virtual element method in presence of corner singularities, Numer. Math. 138 (2018), no. 3, 581–613, DOI: 10.1007/s00211-017-0921-7, Preprint

11. L. Beirão da Veiga, A. Chernov, L. Mascotto and A. Russo, Basic principles of hp Virtual Elements on quasiuniform meshes, Math. Models Methods Appl. Sci. 26 (2016), no. 8, 1567–1598, DOI: 10.1142/S021820251650038X, Preprint

12. C. Bierig and A. Chernov, Approximation of probability density functions by the Multilevel Monte Carlo Maximum Entropy method, J. Comput. Physics 314 (2016), 661–681, DOI: 10.1016/j.jcp.2016.03.027, Preprint

    A supplimentary MATLAB package is available here

13. C. Bierig and A. Chernov, Estimation of arbitrary order central statistical moments by the multilevel Monte Carlo Method, Stoch. Partial Differ. Equ. Anal. Comput. 4 (2016), no. 1, 3–40, DOI: 10.1007/s40072-015-0063-9, Preprint

14. A. Chernov and D. Dũng, New explicit-in-dimension estimates for the cardinality of high-dimensional hyperbolic crosses and approximation of functions having mixed smoothness, J. Complexity 32 (2016), no.1, 92–121, DOI: 10.1016/j.jco.2015.09.001, Preprint

15. A. Chernov, T. von Petersdorff, and C. Schwab, Quadrature algorithms for high-dimensional singular integrands on simplices, Numer. Algorithms 70 (2015), no. 4, 847–874, DOI: 10.1007/s11075-015-9977-6, Preprint

    The supplimentary Netlib package na39 (peer-reviewed) is avaliable at www.netlib.org/numeralgo

16. A. Chernov, D. Pham and T. Tran, A shape calculus based method for a transmission problem with random interface, Comput. Math. Appl. 70 (2015), no. 7, 1401–1424, DOI: 10.1016/j.camwa.2015.06.021, Preprint

17. C. Bierig and A. Chernov, Convergence analysis of multilevel Monte Carlo variance estimators and application for random obstacle problems, Numer. Math. 130 (2015), no. 4, 579–613, DOI: 10.1007/s00211-014-0676-3, Preprint

18. A. Chernov and D. Pham, Sparse spectral BEM for elliptic problems with random input data on a spheroid, Adv. Comput. Math. 41 (2015), no. 1, 77–104, DOI: 10.1007/s10444-014-9350-7, Preprint

19. K. Schmidt and A. Chernov, Robust transmission conditions of high order for thin conducting sheets in two dimensions, IEEE Trans. Magn. 50 (2014), no. 2, 41–44, DOI: 10.1109/TMAG.2013.2285437, Preprint

20. A. Chernov and A. Reinarz, Numerical quadrature for high-dimensional singular integrals over parallelotopes, Comput. Math. Appl. 66 (2013), no. 7, 1213–1231

21. A. Chernov and C. Schwab, First order k-th moment Finite Element analysis of nonlinear operator equations with stochastic data, Math. Comp. 82 (2013), no. 284, 1859–1888

22. K. Schmidt and A. Chernov, A unified analysis of transmission conditions for thin conducting sheets in the time-harmonic eddy current model, SIAM J. Appl. Math. 73 (2013), no. 6, 1980–2003

23. A. Chernov and C. Schwab, Sparse space-time Galerkin BEM for the nonstationary heat equation, ZAMM Z. Angew. Math. Mech. 93 (2013), no. 6–7, 403–413

24. A. Chernov, Optimal convergence estimates for the trace of the polynomial L²-projection operator on a simplex, Math. Comp. 81 (2012), no. 278, 765–787

25. A. Chernov and C. Schwab, Exponential convergence of Gauss-Jacobi quadratures for singular integrals over high dimensional simplices, SIAM J. Numer. Anal. 50 (2012), no. 3, 1433–1455

26. A. Chernov, Sparse polynomial approximation in positive order Sobolev spaces with bounded mixed derivatives and applications to elliptic problems with random loading, Appl. Numer. Math. 62 (2012), no. 4, 360–377

27. D. T. Pham, T. Tran, and A. Chernov, Pseudodifferential equations on the sphere with spherical splines, Math. Models Methods Appl. Sci. 21 (2011), no. 9, 1933–1959

28. A. Chernov, T. von Petersdorff, and C. Schwab, Exponential convergence of hp quadrature for integral operators with gevrey kernels, ESAIM Math. Model. Numer. Anal. 45 (2011), no. 3, 387–422

29. A. Chernov and P. Hansbo, An hp-Nitsche’s method for interface problems with nonconforming unstructured finite element meshes, Vol. 76 of Lecture Notes in Computational Science and Engineering, pp. 153–162, Springer, 2011.

30. A. Chernov and C. Schwab, Sparse p-version BEM for first kind boundary integral equations with random loading, Appl. Numer. Math. 59 (2009), no. 11, 2698–2712

31. A. Chernov, Abstract sensitivity analysis for nonlinear equations and applications, in: Numerical Mathematics and Advanced Applications, ENUMATH 2007, pp. 407–414, Springer, Berlin, Heidelberg, 2008.

32. A. Chernov, M. Maischak, and E.P. Stephan, hp-mortar boundary element method for two-body contact problems with friction, Math. Methods Appl. Sci. 31 (2008), no. 17, 2029–2054

33. A. Chernov, M. Maischak, and E.P. Stephan, A priori error estimates for hp penalty BEM for contact problems in elasticity, Comput. Methods Appl. Mech. Engrg. 196 (2007), no. 37–40, 3871–3880

34. A. Chernov and E.P. Stephan, Adaptive BEM for Contact Problems with Friction, in IUTAM Symposium on Computational Methods in Contact Mechanics, Vol. 3 of IUTAM Bookser., pp. 113–122, Springer, Dordrecht, 2007

35. A. Chernov, S. Geyn, M. Maischak, and E. P. Stephan, Finite element/boundary element coupling for two-body elastoplastic contact problems with friction, in: Analysis and Simulation of Contact Problems, Lecture Notes in Applied and Computational Mechanics, Vol. 27, pp. 171–178, Springer, Berlin, Heidelberg, 2006, P. Wriggers, U. Nackenhorst (Eds.)

Publications in conference proceedings

1. A. Chernov and A. Reinarz, Sparse grid approximation spaces for space-time boundary integral formulations of the heat equation, Oberwolfach Report 06/2022 ''Space-Time Methods for Time-Dependent Partial Differential Equations'', 320-322, DOI: 10.14760/OWR-2022-6

2. C. Bierig, A. Chernov and E. M. Schetzke, Multilevel Monte Carlo approximation of moments, covariance functions and the maximum entropy reconstruction, Oberwolfach Report 12/2019 ''Uncertainty Quantification'', 714–717, DOI: 10.14760/OWR-2019-12

3. K. Schmidt and A. Chernov, Robust transmission conditions of high-order for thin conducting sheets, proceeding of WAVES 2011, Vancouver, Canada, pp. 691–694

4. A. Chernov and C. Schwab, Efficient solution of elliptic BIEs with random loading or on a random boundary, Oberwolfach Report 19/2008 ''Analysis of Boundary Element Methods'', 958–961, DOI: 10.14760/OWR-2008-19

5. A. Chernov, p-Sparse BEM for weakly singular integral equation with random data, proceedings of ICIAM 2007, Zurich, Switzerland, 16–20 July 2007

6. A. Chernov and E. P. Stephan, Adaptive hp-version of mortar BEM for two-body contact problems in elasticity. DtN and Uzawa algorithms, proceedings of IABEM 2006, Graz, Austria, 10–12 July 2006

7. A. Chernov, M. Maischak and E. P. Stephan, hp-mortar boundary element method and FE/BE coupling for multibody contact problems with friction, proceedings of ECCM 2006, Lisbon, Portugal, 5–9 June 2006

8. A. Chernov and A. Koldoba, Propagation of the gasless burning wave. Numerical and Mathematical Modeling, proceedings of scientific conference ''Lomonosov Readings'' Moscow, Russia, April 2003

9. A. Chernov and A. Koldoba, Thermal-diffusive instability of the deflagration front, proceedings of XIV Conference ''Theoretical Basis and Construction of Numerical Algorithms for Problems of Mathematical Physics'', Durso, Russia, September 2002

Other publications

1. A. Chernov, A. Debussche and F. Nobile, Numerical methods for random and stochastic partial differential equations, Editorial preface, Stoch. Partial Differ. Equ. Anal. Comput. 4 (2016), no. 1, 1–2, DOI: 10.1007/s40072-016-0073-2

2. A. Chernov and F. Nobile, Numerical methods for uncertainty quantification, Editorial preface, Int. J. Uncertain. Quantif. 5 (2015), no. 3, vi–vii, DOI: 10.1615/Int.J.UncertaintyQuantification.2015014190

3. A. Chernov and C. Schwab, High-order finite element approximation for partial differential equations, Editorial preface, Comput. Math. Appl. 67 (2014), no. 4, 709–711, DOI: 10.1016/j.camwa.2014.01.012

4. A. Chernov, Nonconforming boundary elements and finite elements for interface and contact problems with friction – hp-version for mortar, penalty and Nitsche's methods, PhD Thesis, University of Hannover, 2006

1. Implementation of the Maximum Entropy method by matching generalized moments is available here. An earlier version of this program have been used for numerical experiments published in the paper:
   
   

   C. Bierig and A. Chernov, Approximation of probability density functions by the Multilevel Monte Carlo Maximum Entropy method, J. Comput. Physics 314 (2016), 661–681, DOI: 10.1016/j.jcp.2016.03.027, Preprint

2. Netlib package na39 (peer-reviewed), avaliable at www.netlib.org/numeralgo. This is a supplementary program package for the paper:
   
   

   A. Chernov, T. von Petersdorff, and C. Schwab, Quadrature algorithms for high-dimensional singular integrands on simplices, Numer. Algorithms 70 (2015), no. 4, 847–874, DOI: 10.1007/s11075-015-9977-6, Preprint