Jan Glaubitz

Professional Experience

• starting Spring 2020: Postdoctoral researcher, Department of Mathematics, Dartmouth College, NH, USA

• since 2016: Research assistant, Institute of Computational Mathematics, TU Braunschweig, Germany

• Fall 2018, 2019: Visiting researcher, Dartmouth College, Hanover, NH, USA (1 week each)
• Summer 2017: Visiting researcher, Max Planck Institute for Mathematics, Bonn, Germany (2 months)
• 2011 - 2016: Student assistant, Department of Mathematics, TU Braunschweig, Germany

Education

• 2016: M.Sc. Mathematics, Institute of Computational Mathematics, TU Braunschweig, Germany.
• 2014: B.Sc. Mathematics, Institute of Computational Mathematics, TU Braunschweig, Germany.

Awards

• 2019: Invited participant of the 7th Heidelberg Laureate Forum.
• 2017: "LehrLEO-Award" for outstanding teaching for my seminar in Numerical Methods for Differential Equations.
• 2016: "Preis für studentisches Engagement" sponsored by the Society of Financial and Economic Mathematics of Braunschweig (VBFWM).
• 2016: "Hauptpreis" of the Geman Mathematical Society (DMV) for my master's thesis.

Refereed Journal Articles

1. J. Glaubitz, P. Öffner:
   Stable discretisations of high-order discontinuous Galerkin methods on equidistant and scattered points.
   Applied Numerical Mathematics, 2020.
   ( DOI:10.1016/j.apnum.2019.12.020 | arXiv:2001.00507 [math.NA] )
2. P. Öffner, J. Glaubitz, H. Ranocha:
   Analysis of artificial dissipation of explicit and implicit time-integration methods.
   Accepted in International Journal of Numerical Analysis and Modeling, 2019.
   ( arXiv:1609.02393 [math.NA] )
3. J. Glaubitz:
   Shock capturing by Bernstein polynomials for scalar conservation laws.
   Applied Mathematics and Computation 363 (2019): 124593.
   ( DOI:10.1016/j.amc.2019.124593 | arXiv:1907.04115 [math.NA] )
4. J. Glaubitz, A. Gelb:
   High order edge sensors with l1 regularization for enhanced discontinuous Galerkin methods.
   SIAM Journal of Scientific Computing, 41(2) (2019): A1304-A1330.
   ( DOI:10.1137/18M1195280 | arXiv:1903.03844 [math.NA] )
5. J. Glaubitz, A.C. Nogueira Jr., J.L.S. Almeida, R.F. Cantão, C.A.C. Silva:
   Smooth and compactly supported viscous sub-cell shock capturing for discontinuous Galerkin methods.
   Journal of Scientific Computing, 79 (2019): 249-272.
   ( DOI:10.1007/s10915-018-0850-3 | arXiv:1810.02152 [math.NA] )
6. P. Öffner, J. Glaubitz, H. Ranocha:
   Stability of correction procedure via reconstruction with summation-by-parts operators for Burgers' equation using a polynomial chaos approach.
   ESAIM: Mathematical Modelling and Numerical Analysis, 52.6 (2018): 2215-2245.
   ( DOI:10.1051/m2an/2018072 | arXiv:1703.03561 [math.NA] )
7. H. Ranocha, J. Glaubitz, P. Öffner, T. Sonar:
   Stability of artificial dissipation and modal filtering for flux reconstruction schemes using summation-by-parts operators. 
   Applied Numerical Mathematics, 128 (2018): 1-23.
   ( DOI:10.1016/j.apnum.2018.01.019 | previous version(s): arXiv:1606.00995 [math.NA], arXiv:1606.01056 [math.NA] )
8. J. Glaubitz, P. Öffner, T. Sonar:
   Application of modal filtering to a spectral difference method.
   Mathematics of Computation, 87.309 (2018): 175-207.
   ( DOI:10.1090/mcom/3257 | arXiv:1604.00929 [math.NA] )

Refereed Conference Proceedings

1. J. Glaubitz, P. Öffner, H. Ranocha, T. Sonar:
   Artificial viscosity for correction procedure via reconstruction using summation-by-parts operators.
   XVI International Conference on Hyperbolic Problems: Theory, Numerics, Applications. Springer, Cham (2016): 363-375.
   ( DOI:10.1007/978-3-319-91548-7_28 )

Books

1. J. Glaubitz, D. Rademacher, T. Sonar:
   Lernbuch Analysis 1 - Das Wichtigste ausführlich für Bachelor und Lehramt.
   Springer, 2019. ( DOI:10.1007/978-3-658-26937-1 )

Others

1. H. Ranocha, J. Glaubitz, P. Öffner, T. Sonar:
   Time discretisation and L2 stability of the polynomial summation-by-parts schemes with Runge-Kutta methods.
   ArXiv preprint arXiv:1609.02393 [math.NA] (2016).
2. J. Glaubitz, P. Öffner, H. Ranocha, T. Sonar:
   Enhancing stability of correction procedure via reconstruction using summation-by parts operators II: Modal filtering.
   ArXiv preprint arXiv:1606.01056 [math.NA] (2016).
3. H. Ranocha, J. Glaubitz, P. Öffner, T. Sonar:
   Enhancing stability of correction procedure via reconstruction using summation-by-parts operators I: Artificial dissipation.
   ArXiv preprint arXiv:1606.00995 [math.NA] (2016).

Scientific Talks and Conferences

1. Numerical integration of experimental data.
   7th Heidelberg Laureate Forum, Heidelberg (Germany), September, 2019.
2. Shock capturing in high-order methods for conservation laws.
   Heinrich-Heine University, Düsseldorf (Germany), October, 2018.
3. High order edge sensors with l1 regularisation for enhanced DG methods.
   Advances in PDEs: Theory, Computation and Application to CFD - ICERM, Brown University, Providence, Rhode Island (USA), August, 2018.
4. The principle of discrete least squares in spectral element approximations.
   XVII International Conference on Hyperbolic Problems - University Park, Pennsylvania (USA), June, 2018.
5. Application of discrete least squares approximations to PDE solvers.
   39th Northern German Colloquium on Applied Analysis and Numerical Mathematics - Braunschweig (Germany), June, 2018.
6. A novel DG method using the principle of discrete least squares.
   Numerical analysis group internal seminar - Oxford (UK), October, 2017.
7. How to overcome the Gibbs phenomenon? Modal and nodal filtering.
   Conference on Recent Advances in Analysis and Numerics of Hyperbolic Conservation Laws - Magdeburg (Germany), September, 2016.
8. Modal filtering for CPR methods using SBP operators.
   XVI International Conference on Hyperbolic Problems - Aachen (Germany), August, 2016.
9. Nodal filtering: How to overcome the Gibbs phenomenon?.
   DMV Students' Conference 2016 - Berlin (Germany), July, 2016.
10. Nodal filtering in spectral methods.
    37th Northern German Colloquium on Applied Analysis and Numerical Mathematics - Lübeck (Germany), April, 2016.

Professional Service

• Peer Review of Articles: SIAM Journal of Scientific Computing, Springer Journal of Scientific Computing, Applied Mathematics and Computation, zbMATH.
• TU Braunschweig: Study commission ("Studienkommission") of the Department of Mathematics (since 2012), appointment committees ("Berufungskommissionen") (2013, 2013, 2013, 2014, 2017), examination board ("Prüfungsausschuss") and admissions committee ("Zulassungsausschuss") of the Department of Mathematics (2014 - 2016).
• Professional affiliations: German Mathematical Society (DMV), Society of Applied Mathematics and Mechanics (GAMM), Braunschweigischer Hochschulbund e.V., Society of Financial and Economic Mathematics of Braunschweig (VBFWM).