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 highorder 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
 Numerical analysis
 Highorder numerical methods for hyperbolic conservation laws
 Shock capturing
 Numerical integration
News
My research focuses on numerical analysis.
The mathematical framework of my research shares with research areas known as
 hyperbolic conservation laws
 highorder methods
 shock capturing
 numerical integration
You can find more details from my publications.
Publications
Preprints
 J. Glaubitz:
Constructing positive interpolatory cubature formulas.
Submitted, 2020. A preprint version can be found here: arXiv:2009.11981 [math.NA].
 J. Glaubitz:
Stable highorder cubature formulas for experimental data.
Submitted, 2020. A preprint version can be found here: arXiv:2009.03452 [math.NA].
Refereed Journal Articles
 J. Glaubitz, A. Gelb:
Stabilizing radial basis function methods for conservation laws using weakly enforced boundary conditions.
Journal of Scientific Computing 87, 40 (2021).
( DOI: 10.1007/s10915021014538  arXiv: 2102.00967 [math.NA] )
 J. Glaubitz, E. Meledo, P. Oeffner:
Towards stable radial basis function methods for linear advection problems.
Computers and Mathematics with Applications 85 (2021): 8497.
( DOI: 10.1016/j.camwa.2021.01.012  arXiv: 2101.09623 [math.NA] )
 J. Glaubitz:
Stable high order quadrature rules for scattered data and general weight functions.
SIAM J. Numer. Anal. 58, 2144 (2020).
( DOI: 10.1137/19M1257901  arXiv: 2007.09082 [math.NA] )
 J. Glaubitz, P. Oeffner:
Stable discretisations of highorder discontinuous Galerkin methods on equidistant and scattered points.
Applied Numerical Mathematics 151 (2020): 98118.
( DOI: 10.1016/j.apnum.2019.12.020  arXiv: 2001.00507 [math.NA] )
 P. Oeffner, J. Glaubitz, H. Ranocha:
Analysis of artificial dissipation of explicit and implicit timeintegration methods.
International Journal of Numerical Analysis and Modeling, 17.3 (2020): 332349.
( URL:http://www.math.ualberta.ca/ijnam/Volume172020/No320/20200303.pdf  arXiv: 1609.02393 [math.NA] )
 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] )
 J. Glaubitz, A. Gelb:
High order edge sensors with l1 regularization for enhanced discontinuous Galerkin methods.
SIAM Journal of Scientific Computing, 41(2) (2019): A1304A1330.
( DOI: 10.1137/18M1195280  arXiv: 1903.03844 [math.NA] )
 J. Glaubitz, A.C. Nogueira Jr., J.L.S. Almeida, R.F. Cantao, C.A.C. Silva:
Smooth and compactly supported viscous subcell shock capturing for discontinuous Galerkin methods.
Journal of Scientific Computing, 79 (2019): 249272.
( DOI: 10.1007/s1091501808503  arXiv: 1810.02152 [math.NA] )
 P. Oeffner, J. Glaubitz, H. Ranocha:
Stability of correction procedure via reconstruction with summationbyparts operators for Burgers' equation using a polynomial chaos approach.
ESAIM: Mathematical Modelling and Numerical Analysis, 52.6 (2018): 22152245.
( DOI: 10.1051/m2an/2018072  arXiv: 1703.03561 [math.NA] )
 H. Ranocha, J. Glaubitz, P. Oeffner, T. Sonar:
Stability of artificial dissipation and modal filtering for flux reconstruction schemes using summationbyparts operators.
Applied Numerical Mathematics, 128 (2018): 123.
( DOI: 10.1016/j.apnum.2018.01.019 )
 J. Glaubitz, P. Oeffner, T. Sonar:
Application of modal filtering to a spectral difference method.
Mathematics of Computation, 87.309 (2018): 175207.
( DOI: 10.1090/mcom/3257  arXiv: 1604.00929 [math.NA] )
Refereed Conference Proceedings
 J. Glaubitz, P. Oeffner, H. Ranocha, T. Sonar:
Artificial viscosity for correction procedure via reconstruction using summationbyparts operators.
XVI International Conference on Hyperbolic Problems: Theory, Numerics, Applications. Springer, Cham (2016): 363375
( DOI: 10.1007/9783319915487_28 )
Books

J. Glaubitz:
Shock capturing and highorder methods for hyperbolic conservation laws.
Dissertation. Logos Verlag Berlin, 2020.
( DOI: 10.30819/5084 )

J. Glaubitz, D. Rademacher, T. Sonar:
Lernbuch Analysis 1  Das Wichtigste ausfuehrlich fuer Bachelor und Lehramt.
Springer, 2019.
( DOI: 10.1007/9783658269371 )
An updated version with some corrections can be found here: Lernbuch.
Scientific Software
 J. Glaubitz:
jglaubitz/stability_RBF_CFs (Version v1.0). Zenodo, 2021.
( DOI: 10.5281/zenodo.5086347 )
 J. Glaubitz:
jglaubitz/weakRBF (Version v1.0). Zenodo, 2020.
( DOI: 10.5281/zenodo.4310328 )
 J. Glaubitz:
jglaubitz/stableCFs (Version v1.0). Zenodo, 2020.
( DOI: 10.5281/zenodo.4018138 )
 J. Glaubitz:
jglaubitz/positive_interpolatory_CFs (Version v1.0). Zenodo, 2020.
( DOI: 10.5281/zenodo.4019333 )
Others
 H. Ranocha, J. Glaubitz, P. Oeffner, T. Sonar:
Time discretisation and L2 stability of polynomial summationbyparts schemes with RungeKutta methods.
arXiv, 2016. ( arXiv: 1609.02393 [math.NA] ).
 J. Glaubitz, H. Ranocha, P. Oeffner, T. Sonar:
Enhancing stability of correction procedure via reconstruction using summationbyparts operators II: Modal filtering.
arXiv, 2016. ( arXiv: 1606.01056 [math.NA] ).
 H. Ranocha, J. Glaubitz, P. Oeffner, T. Sonar:
Enhancing stability of correction procedure via reconstruction using summationbyparts operators I: Artificial dissipation.
arXiv, 2016. ( arXiv: 1606.00995 [math.NA] )
Scientific Talks and Conferences

Least Squares Formulas  The Swiss Army Knife of Numerical Integration? (Slides)
SIAM Annual Meeting, virtual, July, 2021.

High Order Edge Sensors with l1 Regularization for Enhanced Discontinuous Galerkin Methods. (Slides)
ICOSAHOM 2020, virtual, July, 2021.

Numerical integration of experimental data.
7th Heidelberg Laureate Forum; Heidelberg (Germany), September, 2019.

Shock capturing in highorder methods for conservation laws.
HeinrichHeine University, Duesseldorf (Germany), October, 2018.

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.

The principle of discrete least squares in spectral element approximations.
XVII International Conference on Hyperbolic Problems; University Park, Pennsylvania (USA), June, 2018.

Application of discrete least squares approximations to PDE solvers.
39th Northern German Colloquium on Applied Analysis and Numerical Mathematics; Braunschweig (Germany), June, 2018.

A novel discontinuous Galerkin method using the principle of discrete least squares.
Numerical analysis group internal seminar; Oxford (UK), October, 2017.

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.

Modal filtering for CPR methods using SBP operators.
XVI International Conference on Hyperbolic Problems; Aachen (Germany), August, 2016.

Nodal filtering: How to overcome the Gibbs phenomenon?
DMV Students' Conference 2016; Berlin (Germany), July, 2016.

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.
 Summer 2019: Catastrophe Theory
 Winter 2018: Mathematics for Electrical Engineers III
 Summer 2018: Mathematics for Electrical Engineers II
 Summer 2018: Seminar  Differential Equations and Vector Calculus
 Winter 2017: Seminar in Analysis
 Winter 2017: Dynamical Systems
 Summer 2017: Analysis II
 Summer 2017: Seminar in Analysis
 Winter 2017: Analysis I
 Summer 2016: Numerical Methods for Differential Equations
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.
 Winter 2015: Analysis III
 Summer 2015: Preparation Course in Mathematics
 Summer 2015: Linear Algebra II
 Winter 2014: Linear Algebra I
 Summer 2014: Preparation Course in Mathematics
 Summer 2014: Numerical Methods for Ordinary Differential Equations
 Summer 2014: Analysis II
 Winter 2013: Analysis I
 Summer 2013: Preparation Course in Mathematics
 Summer 2013: Mathematics for Electrical Engineers II
 Winter 2012: Mathematics for Electrical Engineers I
 Summer 2012: Preparation Course in Mathematics
 Summer 2012: Mathematics for Electrical Engineers II
 Winter 2011: Mathematics for Electrical Engineers I
 Summer 2011: Preparation Course in Mathematics
Student Supervision
 Bachelor's thesis advisor for Franziska Keilmann, 2018.
Using Discrete Least Squares Approximations in the Gegenbauer Reconstruction Method,
Lecture Notes
 Spring 2021: Introduction to Applied Mathematics
 Spring 2020: Introduction to Applied Mathematics