TU Darmstadt | Fachbereich Mathematik | Research Group Numerical Analysis and Scientific Computing

Research Group
Numerical Analysis and Scientific Computing

List of Publications
Prof. Dr. Jan Giesselmann


List of Publications  |  List of Recent Publications  |  Last update: 26.06.2025 14:41.

Preprints (6)

2025
and : "A posteriori error control for a finite volume scheme for a cross-diffusion model of ion transport", arXiv, 2025. [doi]
and : "Extending relative entropy for Korteweg-type models with non-monotone pressure:large friction limit and weak-strong uniqueness", arXiv, 2025. [doi]
2024
; ; and : "Error analysis of a first-order DoD cut cell method for 2D unsteady advection", arXiv, 2024. [doi]
; and : "Robust a posteriori error control for the Allen-Cahn equation with variable mobility", arXiv, 2024. [doi]
and : "Identification of minimal number of measurements allowing synchronization of a nodal observer for the wave equation", arXiv, 2024. [doi]
2023
and : "Regularity and long time behavior of a doubly nonlinear parabolic problem and its discretization", arXiv, 2023. [doi]

Refereed Articles (43)

2025
; and : "Energy-consistent Petrov-Galerkin time discretization of port-Hamiltonian systems", SMAI J. Comp. Math., vol. 11, pp. 335–367, 2025. [doi] [preprint]
and : "A-posteriori error estimates for systems of hyperbolic conservation laws via computing negative norms of local residuals", IMA J. Numer. Anal., pp. drae111, 2025. [doi] [preprint]
2024
; and : "Numerical discretisation of hyperbolic systems of moment equations describing sedimentation in suspensions of rod-like particles", J. Comp. Phys., pp. 113162, 2024. [doi] [preprint]
and : "Improving Weak PINNs for Hyperbolic Conservation Laws: Dual Norm Computation, Boundary Conditions and Systems", SMAI J. Comput. Math., vol. 10, pp. 373–401, 2024. [doi] [preprint]
; and : "Observer-based data assimilation for barotropic gas transport using distributed measurements", Comm. Math. Sci., vol. 22, no. 8, pp. 2271-2309, 2024. [doi] [preprint]
and : "Theory of shifts, shocks, and the intimate connections to $L^2$-type a posteriori error analysis of numerical schemes for hyperbolic problems", Math. Comp., 2024. [doi] [preprint]
and : "A posteriori error control for a Discontinuous Galerkin approximation of a Keller-Segel model", Adv. Comp. Math., vol. 50, no. 119, 2024. [doi] [preprint]
and : "An Observer for Pipeline Flow with Hydrogen Blending in Gas Networks: Exponential Synchronization", SIAM J. Control Optim., vol. 62, no. 4, pp. 2273-2296, 2024. [doi] [preprint]
and : "A priori error estimates of Runge Kutta discontinuous Galerkin schemes to smooth solutions of fractional conservation laws", M2AN Math. Model. Numer. Anal., vol. 58, no. 4, pp. 1301–1315, 2024. [doi] [preprint]
and : "Stability of step size control based on a posteriori error estimates", Comput. Sci. Eng., vol. 1, no. 1, 2024. [doi] [preprint]
; and : "Data-driven snapshot calibration via monotonic feature matching", Finite Elem. Anal. Des., vol. 230, pp. 104065, 2024. [doi]
and : "A posteriori error analysis of a positivity preserving scheme for the power-law diffusion Keller–Segel model", IMA J. Numer. Anal., pp. drae073, 2024. [doi] [preprint]
2023
; and : "On the convergence of the regularized entropy-based moment method for kinetic equations", SMAI J. Comput. Math., vol. 9, pp. 1–29, 2023. [doi] [preprint]
and : "Stability and asymptotic analysis for instationary gas transport via relative energy estimates", Numer. Math., 2023. [doi] [preprint]
; and : "A posteriori error estimates for wave maps into spheres", Adv. Comput. Math., vol. 49, 2023. [doi] [preprint]
2022
; ; and : "An asymptotic-preserving discretization scheme for gas transport in pipe networks", IMA J. Numer. Anal., 2022. [doi] [preprint]
2021
; ; and : "Residual estimates for post-processors in elliptic problems", J. Sci. Comput., vol. 88, no. 2, pp. Paper No. 34, 28, 2021. [doi] [preprint]
; and : "Error control for statistical solutions of hyperbolic systems of conservation laws", Calcolo, vol. 58, no. 2, pp. Paper No. 23, 29, 2021. [doi] [preprint]
and : "Boundary feedback stabilization of a semilinear model for the flow in star-shaped gas networks", ESAIM Control Optim. Calc. Var., vol. 27, pp. Paper No. 67, 24, 2021. [doi]
; and : "Exponential synchronization of a nodal observer for a semilinear model for the flow in gas networks", IMA J. Math. Control Inform., vol. 38, no. 4, pp. 1109–1147, 2021. [doi] [preprint]
2020
and : "Formulation and convergence of the finite volume method for conservation laws on spacetimes with boundary", Numer. Math., vol. 144, no. 4, pp. 751–785, 2020. [doi] [preprint]
; and : "A posteriori error analysis and adaptive non-intrusive numerical schemes for systems of random conservation laws", BIT, vol. 60, no. 3, pp. 619–649, 2020. [doi] [preprint]
; and : "A posteriori error analysis for random scalar conservation laws using the stochastic Galerkin method", IMA J. Numer. Anal., vol. 40, no. 2, pp. 1094–1121, 2020. [doi] [preprint]
; and : "Convergence analysis of Grad's Hermite expansion for linear kinetic equations", SIAM J. Numer. Anal., vol. 58, no. 2, pp. 1164–1194, 2020. [doi] [preprint]
2018
; ; and : "Existence and uniqueness of global classical solutions to a two dimensional two species cancer invasion haptotaxis model", Discrete Contin. Dyn. Syst. Ser. B, vol. 23, no. 10, pp. 4397–4431, 2018. [doi] [preprint]
2017
; and : "Relative energy for the Korteweg theory and related Hamiltonian flows in gas dynamics", Arch. Ration. Mech. Anal., vol. 223, no. 3, pp. 1427–1484, 2017. [doi] [preprint]
and : "A posteriori analysis for dynamic model adaptation in convection-dominated problems", Math. Models Methods Appl. Sci., vol. 27, no. 13, pp. 2381–2423, 2017. [doi] [preprint]
and : "Stability properties of the Euler-Korteweg system with nonmonotone pressures", Appl. Anal., vol. 96, no. 9, pp. 1528–1546, 2017. [doi] [preprint]
2016
and : "A posteriori analysis of fully discrete method of lines discontinuous Galerkin schemes for systems of conservation laws", SIAM J. Numer. Anal., vol. 54, no. 6, pp. 3523–3549, 2016. [doi] [preprint]
: "Relative entropy based error estimates for discontinuous Galerkin schemes", Bull. Braz. Math. Soc. (N.S.), vol. 47, no. 1, pp. 359–372, 2016. [doi]
and : "Reduced relative entropy techniques for a priori analysis of multiphase problems in elastodynamics", BIT, vol. 56, no. 1, pp. 99–127, 2016. [doi] [preprint]
2015
: "Low Mach asymptotic-preserving scheme for the Euler-Korteweg model", IMA J. Numer. Anal., vol. 35, no. 2, pp. 802–833, 2015. [doi] [preprint]
: "Relative entropy in multi-phase models of 1d elastodynamics: convergence of a non-local to a local model", J. Differential Equations, vol. 258, no. 10, pp. 3589–3606, 2015. [doi] [preprint]
; and : "A posteriori analysis of discontinuous Galerkin schemes for systems of hyperbolic conservation laws", SIAM J. Numer. Anal., vol. 53, no. 3, pp. 1280–1303, 2015. [doi] [preprint]
and : "Energy consistent discontinuous Galerkin methods for a quasi-incompressible diffuse two phase flow model", ESAIM Math. Model. Numer. Anal., vol. 49, no. 1, pp. 275–301, 2015. [doi] [preprint]
2014
; ; and : "A quasi-incompressible diffuse interface model with phase transition", Math. Models Methods Appl. Sci., vol. 24, no. 5, pp. 827–861, 2014. [doi]
; and : "A compressible mixture model with phase transition", Phys. D, vol. 273/274, pp. 1–13, 2014. [doi]
: "A relative entropy approach to convergence of a low order approximation to a nonlinear elasticity model with viscosity and capillarity", SIAM J. Math. Anal., vol. 46, no. 5, pp. 3518–3539, 2014. [doi]
; and : "Energy consistent discontinuous Galerkin methods for the Navier-Stokes-Korteweg system", Math. Comp., vol. 83, no. 289, pp. 2071–2099, 2014. [doi] [preprint]
and : "Geometric error of finite volume schemes for conservation laws on evolving surfaces", Numer. Math., vol. 128, no. 3, pp. 489–516, 2014. [doi] [preprint]
and : "Singular limiting induced from continuum solutions and the problem of dynamic cavitation", Arch. Ration. Mech. Anal., vol. 212, no. 1, pp. 241–281, 2014. [doi] [preprint]
2012
; ; and : "Asymptotic analysis for Korteweg models", Interfaces Free Bound., vol. 14, no. 1, pp. 105–143, 2012. [doi]
2009
: "A convergence result for finite volume schemes on Riemannian manifolds", M2AN Math. Model. Numer. Anal., vol. 43, no. 5, pp. 929–955, 2009. [doi]

Book Chapters (14)

2024
; ; and : "Model Adaptation for Hyperbolic Balance Laws", Chapter in Hyperbolic Problems: Theory, Numerics, Applications. Volume II (Parés, Carlos; Castro, Manuel J.; Morales de Luna, Tomás; Muñoz-Ruiz, María Luz, eds.), Springer Nature Switzerland, pp. 73–83, 2024.
2020
and : "Model adaptation of balance laws based on a posteriori error estimates and surrogate fluxes", Chapter in Finite volumes for complex applications IX—methods, theoretical aspects, examples—FVCA 9, Bergen, Norway, June 2020, Springer, Cham, pp. 375–383, 2020. [doi]
2018
and : "Residual error indicators for discontinuous Galerkin schemes for discontinuous solutions to systems of conservation laws", Chapter in Theory, numerics and applications of hyperbolic problems. I, Springer, Cham, pp. 459–471, 2018. [doi]
and : "A posteriori analysis for the Euler-Korteweg model", Chapter in Theory, numerics and applications of hyperbolic problems. I, Springer, Cham, pp. 631–642, 2018. [doi]
2017
and : "Goal-oriented error analysis of a DG scheme for a second gradient elastodynamics model", Chapter in Finite volumes for complex applications VIII—methods and theoretical aspects, Springer, Cham, pp. 457–466, 2017. [doi]
2014
; and : "The problem of dynamic cavitation in nonlinear elasticity", Chapter in Séminaire Laurent Schwartz—Équations aux dérivées partielles et applications. Année 2012–2013, École Polytech., Palaiseau, pp. Exp. No. XIV, 17, 2014.
and : "Estimating the geometric error of finite volume schemes for conservation laws on surfaces for generic numerical flux functions", Chapter in Finite volumes for complex applications VII. Methods and theoretical aspects, Springer, Cham, pp. 323–331, 2014. [doi]
and : "On aposteriori error analysis of dG schemes approximating hyperbolic conservation laws", Chapter in Finite volumes for complex applications VII. Methods and theoretical aspects, Springer, Cham, pp. 313–321, 2014. [doi]
and : "On cavitation in elastodynamics", Chapter in Hyperbolic problems: theory, numerics, applications, Am. Inst. Math. Sci. (AIMS), Springfield, MO, pp. 599–606, 2014. [preprint]
2013
and : "Finite volume schemes for balance laws on time-dependent surfaces", Chapter in Numerical methods for hyperbolic equations: theory and applications, CRC Press/Balkema, Leiden, pp. 251–258, 2013. [doi]
2012
; ; ; ; and : "A diffuse interface model for quasi-incompressible flows: sharp interface limits and numerics", Chapter in CEMRACS'11: Multiscale coupling of complex models in scientific computing, EDP Sci., Les Ulis, pp. 54–77, 2012. [doi]
; ; ; ; ; ; ; and : "Sediment transport modelling: relaxation schemes for Saint-Venant–Exner and three layer models", Chapter in CEMRACS'11: Multiscale coupling of complex models in scientific computing, EDP Sci., Les Ulis, pp. 78–98, 2012. [doi]
: "Sharp interface limits for Korteweg models", Chapter in Hyperbolic problems—theory, numerics and applications. Volume 2, World Sci. Publishing, Singapore, pp. 422–430, 2012.
2008
: "Convergence rate of finite volume schemes for hyperbolic conservation laws on Riemannian manifolds", Chapter in Finite volumes for complex applications V, ISTE, London, pp. 463–470, 2008.
Impressum | Datenschutzerklärung