Numerical methods for hyperbolic conservation laws
Shock capturing
Edge and shock detection
Viscosity terms and their discretization
Professional Experience
since 2016: Research assistant, Institute of Computational Mathematics, TU Braunschweig, Germany (Thomas Sonar, Ph.D. advisor).
Fall 2018: Visiting researcher, Dartmouth College, Hanover, NH, USA (1 week).
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.
Publications
Preprints
J. Glaubitz: Stable High-Order Quadrature Rules for Scattered Data and General Weight Functions. Submitted, 2019.
J. Glaubitz, P. Öffner: Stable Discretisations of High-Order Discontinuous Galerkin Methods on Equidistant and Arbitrary Points, Submitted, 2019.
J. Glaubitz, P. Öffner, H. Ranocha: Analysis of Artificial Dissipation of Explicit and Implicit Time-Integration Methods, Submitted, 2018.
J. Glaubitz: Shock Capturing by Bernstein Polynomials for Scalar Conservation Laws, Submitted, 2018.
J. Glaubitz: Discrete Least Squares Quadrature Rules on Equidistant and Arbitrary Points, Submitted, 2018. ( MPIM preprint series: 2018-23 | bibtex )
J. Glaubitz, P. Öffner: A Novel Discontinuous Galerkin Method Using the Principle of Discrete Least Squares, Submitted, 2017. ( MPIM preprint series: 2017-63 | bibtex )
Refereed Journal Articles
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] )
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] )
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] )
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] )
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
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
J. Glaubitz, D. Rademacher, T. Sonar: Lernbuch Analysis 1. Springer (to appear 2019).
Others
H. Ranocha, J. Glaubitz, P. Öffner, T. Sonar: Time discretisation and L2 stability of the polynomial summation-by-parts schemes with Runge-Kutta method. ArXiv preprint arXiv:1609.02393 [math.NA] (2016).
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).
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
Shock Capturing in High-Order Methods for Conservation Laws. Heinrich-Heine University, Düsseldorf (Germany), October, 2018.
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.
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 DG 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 - Lübeck (Germany), April, 2016.
Teaching Activities
Courses taught
2016 - : TU Braunschweig, research assistant: I designed and held tutorials (up to 200 students) and organized student assistants for more than 6 undergraduate and graduate courses 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 (complex analysis and distribution theory)
Summer 2018: Mathematics for Electrical Engineers II (analysis in several variables and vector analysis)
Summer 2018: Seminar - Differential Equations and Vector Calculus
Winter 2017: Seminar - Analysis
Winter 2017: Dynamical Systems
Summer 2017: Analysis II (analysis in several variables and ordinary differential equations)
Summer 2017: Seminar - Analysis
Winter 2017: Analysis I (analysis in one dimension)
Summer 2016: Numerical Methods for Differential Equations (interpolation, numerical integration, and discretizations of ordinary and partial differential equations)
2011 - 2016: TU Braunschweig, student assistant: 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 (vector analysis and ordinary differential equations)
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 (analysis in several variables and measure and integration theory)
Winter 2013: Analysis I (analysis in one dimension)
Summer 2013: Preparation Course in Mathematics
Summer 2013: Mathematics for Electrical Engineers II (analysis in several variables and vector analysis)
Winter 2012: Mathematics for Electrical Engineers I (analysis and linear algebra)
Summer 2012: Preparation Course in Mathematics
Summer 2012: Mathematics for Electrical Engineers II (analysis in several variables and vector analysis)
Winter 2011: Mathematics for Electrical Engineers I (analysis and linear algebra)
Summer 2011: Preparation Course in Mathematics
Student Supervision
Bachelor’s thesis advisor for Franziska Keilmann, Using Discrete Least Squares Approximations in the Gegenbauer Reconstruction Method, B.Sc., 2018.
Professional Service
Peer Review of Articles: SIAM Journal of Scientific Computing, Springer Journal of Scientific Computing.
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).