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 students

Alumni

Postdoctoral research fellows

PhD students

• Lourenço Beirão da Veiga, University of Milano-Bicocca, Italy
• Claudio Bierig, University of Oldenburg, Germany
• Dinh Dũng, Vietnam National University, Hanoi, Vietnam
• Herbert Egger, TU Darmstadt, Germany
• Matthias Maischak, Brunel University, United Kingdom
• Lorenzo Mascotto, University of Vienna, Austria
• Duong T. Pham, Vietnamese-German University, Vietnam
• Anne Reinarz, TU Munich, Germany
• Alessandro Russo, University of Milano-Bicocca, Italy
• Erik M. Schetzke, University of Oldenburg, Germany
• Kersten Schmidt, TU Berlin, Germany
• Christoph Schwab, ETH Zurich, Switzerland
• 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, H. Hoel, K. Law, F. Nobile and R. Tempone, Multilevel ensemble Kalman filtering for spatially extended models, August 2016, submitted, available online: Preprint

Peer-reviewed Publications

1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

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

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. D. 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

18. 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

19. 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.

20. 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

21. 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.

22. 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

23. 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

24. 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

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

2. 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'', 6–9

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

4. 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

5. 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

6. 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

7. 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