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Lehre an der Uni Hamburg (SoSe 2022)
Seminar über Approximation
Numerik von partiellen Differentialgleichungen - Finite Differenzen und Finite Volumen (Vorlesung und Übungen)

Sprechstunde an der Uni Hamburg (SoSe 2022)
Mo., 10:00 - 11:00, Raum 1509
oder nach Vereinbarung

Frühere Lehre
Analysis I und II(Übungen und Tutorium)
Approximation (Vorlesung und Übungen)
Funktionalanalysis (Übungen)
Numerik von partiellen Differentialgleichungen (Vorlesung und Übungen)
Analysis I - III für Ingenieure (Übungen, TUHH)
Gewöhnliche Differentialgleichungen für Ingenieure (Übungen, TUHH)
Partielle Differentialgleichungen für Ingenieure (Übungen, TUHH)

Theoretische und numerische Behandlung von Evolutionsgleichungen, insbesondere hyperbolische Erhaltungsgleichungen. Numerische Analysis für Finite Volumen und unstetige Galerkin Methoden hoher Ordnung, verallgemeinerte Riemann Probleme, WENO Verfahren, Entropiestabilität

Claus R. Goetz, Dinshaw S. Balsara, Michael Dumbser: A family of HLL-type solvers for the generalized Riemann problem,
Computers and Fluids 169 (2018) pp. 201-212

Claus R. Goetz, Michael Dumbser: A square entropy stable flux limiter for PNPM schemes,
preprint (2016)

Claus R. Goetz, Michael Dumbser: A novel solver for the generalized Riemann problem based on a simplified LeFloch-Raviart expansion and a local space-time discontinuous Galerkin formulation,
J. Sci. Comput. 69 (2016), pp. 805 - 840

Claus R. Goetz, Armin Iske: Approximate solutions of generalized Riemann problems for nonlinear systems of hyperbolic conservation laws,
Math. Comp. 85, No 297 (2016), pp. 35-62 (preprint)

Claus R. Goetz, Armin Iske: Approximate solutions of generalized Riemann problems: The Toro-Titarev solver and the LeFloch-Raviart expansion ,
Numerical Methods for Hyperbolic Equations: Theory and Applications, M. E. Vásques-Cedón and A. Hidalgo and P. García-Navarro and L. Cea, eds., Taylor-Francis Group, 2013, pp. 267 - 275

Dissertation:
Approximate Solutions of Generalized Riemann Problems for Hyperbolic Conservation Laws and Their Application to High Order Finite Volume Schemes ,
Universität Hamburg, 2013 (Volltext bei der Staats- und Universitätsbibliothek Hamburg)

Applied and Computational Mathematics Seminar (invited speaker) (UC Dublin), November 11, 2019, Dublin (IRL),

International Conference on Spectral and High Order Methods (ICOSAHOM 2018), July 9-13, 2018, London (UK),

XVII International Conference on Hyperbolic Problems Theory, Numerics, Applications (HYP 2018) June 25-29, 2018, University Park, PN (USA)

European Conference on High Order Nonlinear Numerical Methods for Evolutionary PDEs: Theory and Applications (HONOM 2017), March 27-31, 2017, Stuttgart (Germany),
Talk: A square entropy stable flux limiter for PNPM schemes

Recent trends and future developments in Computational Science and Engineering, Workshop of the Lothar Collatz Center (LCS-CSE), March 22 -24, 2017, Plön (Germany),
Talk: A family of HLL-type solvers for the generalized Riemann problem

Fifth Chilean Workshop on Numerical Analysis of Partial Differential Equations ( WONAPDE2016 ), January 11-15, 2016, Concepción (Chile),
Talk: An ADER scheme with a new solver for the generalized Riemann problem and local space-time DG flux integration

European Conference on High Order Nonlinear Numerical Methods for Evolutionary PDEs: Theory and Applications (HONOM 2015), March 16-20, 2015, Trento (Italy),
Talk: A novel GRP solver for the ADER method based on a simplified LeFloch-Ravaiart expansion

Modern Perspectives in Applied Mathematics: Theory and Numerics of PDEs, A Conference in Honor of Eitan Tadmor's 60th Birthday (TN60), April 28 - May 2, 2014, Bethesda, MD (USA)

European Conference on High Order Nonlinear Numerical Methods for Evolutionary PDEs: Theory and Applications (HONOM 2013), March, 18-22, 2013, Bordeaux (France),
Talk: Approximate solutions of generalized Riemann problems for nonlinear systems of hyperbolic conservation laws.

Numerical Methods for Hyperbolic Equations: Theory and Applications, International Conference to honour Professor E.F. Toro in the month of his 65th birthday (NMHETATORO65), July 4-8, Santiago de Compostela (Spain),
Talk: The Toro-Titarev solver and the LeFloch-Raviart expansion for the generalized Riemann problem.

European Conference on High Order Nonlinear Numerical Methods for Evolutionary PDEs: Theory and Applications (HONOM 2011), April 11-15, 2011, Trento (Italy),
Talk: On the Analysis of a Solver for Genaralized Riemann Problems by Asymptotic Expansion.