Jan Glaubitz

Jan Glaubitz


Department of Mathematics
Dartmouth College
27 North Main Street
Hanover, NH 03755, USA

Office : 335 Kemeny Hall
Email : Jan.Glaubitz at Dartmouth.edu

I am a postdoctoral researcher in the working group of Anne Gelb at the Department of Mathematics, Dartmouth College. My research focuses on numerical analysis and high-order methods for hyperbolic conservation laws.

Before joining Dartmouth, I completed my mathematical studies (B.Sc., 2014, M.Sc., 2016, Dr. rer. nat., 2019) at TU Braunschweig in Germany.

Research Interests

News

Dissertation - Jan Glaubitz

Professional Experience

Education

Awards

Support

Professional Service

My CV is available for download here [link]!

My research focuses on numerical analysis.

The mathematical framework of my research shares with research areas known as

You can find more details from my publications.

Publications

Preprints

  1. J. Glaubitz, A. Gelb:
    Stability of radial basis function methods for one dimensional scalar conservation laws in weak form.
    Submitted, 2019.
  2. J. Glaubitz:
    Stable high order quadrature rules for scattered data and general weight functions.
    Submitted, 2019.
  3. J. Glaubitz: Discrete least squares quadrature rules on equidistant and arbitrary points.
    Submitted, 2018.

Refereed Journal Articles

  1. J. Glaubitz, P. Oeffner:
    Stable discretisations of high-order discontinuous Galerkin methods on equidistant and scattered points.
    Applied Numerical Mathematics 151 (2020): 98-118.
    ( DOI: 10.1016/j.apnum.2019.12.020 | arXiv: 2001.00507 [math.NA] )
  2. P. Oeffner, 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. Cantao, 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. Oeffner, 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. Oeffner, 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 )
  8. J. Glaubitz, P. Oeffner, 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. Oeffner, 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

Dissertation - Jan Glaubitz Lernbuch - Jan Glaubitz
  1. J. Glaubitz:
    Shock capturing and high-order methods for hyperbolic conservation laws.
    Dissertation. Logos Verlag Berlin, 2020.
    ( DOI: 10.30819/5084 )
  2. J. Glaubitz, D. Rademacher, T. Sonar:
    Lernbuch Analysis 1 - Das Wichtigste ausfuehrlich fuer Bachelor und Lehramt.
    Springer, 2019.
    ( DOI: 10.1007/978-3-658-26937-1 )

Others

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

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, Duesseldorf (Germany), October, 2018.
  3. High order edge sensors with l1 regularisation for enhanced discontinuous Galerkin 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 discontinuous Galerkin 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; Luebeck (Germany), April, 2016.

Courses Taught


Dartmouth College, postdoctoral researcher (since 2020):

I design and give lectures as well as exercises for graduate and undergraduate students.

TU Braunschweig, research assistant (2016 - 2020):

I designed and held tutorials (up to 200 students) and organized student assistants for 10 undergraduate and graduate courses and seminars in numerical methods for differential equations, analysis, dynamical systems, and mathematics for electrical engineers.

TU Braunschweig, student assistant (2011 - 2016):

I held exercise tutorials (up to 20 students) for 15 undergraduate courses for mathematicians and engineers in analysis, linear algebra, and numerical methods for ordinary differential equations.

Student Supervision

  1. Bachelor's thesis advisor for Franziska Keilmann, 2018.
    Using Discrete Least Squares Approximations in the Gegenbauer Reconstruction Method,