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

Research Group
Numerical Analysis and Scientific Computing

List of Recent Publications


List of Publications  |  List of Recent Publications  |  Last update: 13.12.2024 08:16.

Preprints (8)

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 : "Exact Integration for singular Zienkiewicz and Guzman-Neilan Finite Elements with Implementation", arXiv, 2024. [doi]
; and : "Energy-consistent Petrov-Galerkin time discretization of port-Hamiltonian systems", 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 : "Grading of triangulations generated by bisection", arXiv, 2023. [doi]
and : "Regularity and long time behavior of a doubly nonlinear parabolic problem and its discretization", arXiv, 2023. [doi]
and : "A-posteriori error estimates for systems of hyperbolic conservation laws", arXiv, 2023. [doi]

Refereed Articles (54)

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 : "Novel Aspects in Pattern Formation Arise from Coupling Turing Reaction–Diffusion and Chemotaxis", Bull Math Biol, vol. 86, pp. (published online 1 Dec 2023), 2024. [doi]
and : "Implicit peer triplets in gradient-based solution algorithms for ODE constrained optimal control", J. Optim. Theory Appl, 2024. [doi]
and : "A priori error estimates of Runge Kutta discontinuous Galerkin schemes to smooth solutions of fractional conservation laws", M2AN Math. Model. Numer. Anal., 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 : "Dimensions of Exactly Divergence-Free Finite Element Spaces in 3D", SIAM J. Sci. Comput., vol. 46, no. 2, pp. A1102–A1131, 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 : "Numerical solution of differential and differential-algebraic equations. Selected papers from NUMDIFF-16 [Preface]", J. Comput. Appl. Math., vol. 430, 2023. [doi]
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]
and : "Exact discrete solutions of boundary control problems for the 1D heat equation", J. Optim. Theory Appl, vol. 196, pp. 1106–1118, 2023. [doi]
; ; and : "Physics informed neural networks: A case study for gas transport problems", J. Comput. Phys., vol. 481, pp. 112041, 2023. [doi]
2022
; and : "Fortin operator for the Taylor-Hood element", Numer. Math., vol. 150, no. 2, pp. 671–689, 2022. [doi] [preprint]
; and : "Fast and reliable transient simulation and continuous optimization of large-scale gas networks", Math. Methods Oper. Res., vol. 95, no. 3, pp. 475–501, 2022. [doi]
; ; ; and : "Adapted Contour Integration for Nonlinear Eigenvalue Problems in Waveguide Coupled Resonators", IEEE Trans. Antennas and Propagation, vol. 70, no. 1, pp. 499-513, 2022. [doi]
; and : "Shape optimization in acoustic–structure interaction", Eng. Computations, vol. 39, no. 1, pp. 172–200, 2022. [doi]
and : "Discrete adjoint implicit peer methods in optimal control", J. Comput. Appl. Math., vol. 416, pp. Paper No. 114596, 15, 2022. [doi]
and : "Implicit A-stable peer triplets for ODE constrained optimal control problems", Algorithms, vol. 15, pp. 310, 2022. [doi]
; ; and : "Homogenization of the time-dependent heat equation on planar one-dimensional periodic structures", Appl. Anal., Taylor & Francis, vol. 101, no. 12, pp. 4046–4075, 2022. [doi]
; and : "A class of boundary conditions for time-discrete Green-Naghdi equations with bathymetry", SIAM J. Numer. Anal., vol. 60, no. 5, pp. 2681–2712, 2022. [doi] [preprint]
and : "Impedance boundary conditions for acoustic time harmonic wave propagation in viscous gases in two dimensions", Math. Meth. Appl. Sci., vol. 45, no. 12, pp. 7404–7425, 2022. [doi]
; ; and : "Probabilistic constrained optimization on flow networks", Optim. Eng., vol. 23, no. 2, pp. 983–1032, 2022. [doi]
; and : "A novel nonlocal partial differential equation model of endothelial progenitor cell cluster formation during the early stages of vasculogenesis", J Theor Biol, vol. 534, pp. 110963, 2022. [doi] [preprint]
; ; and : "An asymptotic-preserving discretization scheme for gas transport in pipe networks", IMA J. Numer. Anal., 2022. [doi] [preprint]
2021
; ; ; ; and : "Numerical solution of differential and differential-algebraic equations. Selected papers from NUMDIFF-15 [Preface]", J. Comput. Appl. Math., vol. 387, pp. Paper No. 112611, 2, 2021. [doi]
; ; 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 : "On the Sobolev and $L^p$-stability of the $L^2$-projection", SIAM J. Numer. Anal., vol. 59, no. 5, pp. 2571–2607, 2021. [doi] [preprint]
; and : "Multistep and Runge-Kutta convolution quadrature methods for coupled dynamical systems", J. Comput. Appl. Math., vol. 387, pp. 112618, 2021. [doi]
and : "A third-order weighted essentially non-oscillatory scheme in optimal control problems governed by nonlinear hyperbolic conservation laws", Comput. Optim. Appl., vol. 80, no. 1, pp. 301–320, 2021. [doi]
; 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]
; and : "Conditioning of implicit Runge-Kutta integration for finite element approximation of linear diffusion equations on anisotropic meshes", J. Comput. Appl. Math., vol. 387, pp. Paper No. 112497, 17, 2021. [doi]
and : "A local radial basis function differential quadrature semi-discretisation technique for the simulation of time-dependent reaction-diffusion problems", Engineering Computations, vol. 38, no. 6, pp. 2666-2691, 2021. [doi]
; ; ; and : "Uncertainty Quantification Guided Parameter Selection in a Fully Coupled Molecular Dynamics-Finite Element Model of the Mechanical Behavior of Polymers", J. Chem. Theory Comput., vol. 17, no. 6, pp. 3760-3771, 2021. [doi]
; and : "Super-convergent implicit-explicit Peer methods with variable step sizes", J. Comput. Appl. Math., vol. 387, pp. Paper No. 112501, 16, 2021. [doi]
; ; ; and : "Quantification of bore path uncertainty in borehole heat exchanger arrays using adaptive anisotropic stochastic collocation", Geothermics, vol. 97, no. 4, pp. 102194, 2021. [doi]
; and : "Stochastic Galerkin Reduced Basis Methods for Parametrized Linear Convection-Diffusion-Reaction Equations", Fluids, vol. 6, pp. 263, 2021. [doi]
; ; and : "Mechanical Models of Pattern and Form in Biological Tissues: The Role of Stress–Strain Constitutive Equations", Bull Math Biol, vol. 83, pp. Article 80, 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 fully adaptive multilevel stochastic collocation strategy for solving elliptic PDEs with random data", J. Comput. Phys., vol. 419, pp. 109692, 17, 2020. [doi]
; 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]
and : "Fully discrete finite element approximation of unsteady flows of implicitly constituted incompressible fluids", IMA J. Numer. Anal., vol. 40, no. 2, pp. 801–849, 2020. [doi] [preprint]
; and : "An adaptive moving finite element method for steady low Mach number compressible combustion problems", Internat. J. Numer. Methods Fluids, vol. 92, no. 9, pp. 1081–1095, 2020. [doi]
; ; ; ; ; ; ; ; ; ; and : "In vitro and in silico modeling of cellular and matrix-related changes during the early phase of osteoarthritis", Biofabrication, vol. 12, pp. 045016, 2020. [doi]

Book Chapters (6)

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.
2022
; and : "Adaptive single- and multilevel stochastic collocation methods for uncertain gas transport in large-scale networks", Chapter in Mesh generation and adaptation—cutting-edge techniques, Springer, Cham, pp. 113–135, 2022. [doi]
2021
: "Rosenbrock-Wanner methods: construction and mission", Chapter in Rosenbrock–Wanner-type methods—theory and applications, Springer, Cham, pp. 1–17, 2021. [doi]
and : "Well-balanced and asymptotic preserving IMEX-peer methods", Chapter in Numerical mathematics and advanced applications—ENUMATH 2019, Springer, Cham, pp. 861–870, 2021.
and : "Multi-Scale Analysis of Contact-Dependent Interaction in Tissue Aggregation and Invasion", Chapter in Systems Medicine: Integrative, Qualitative and Computational Approaches (Wolkenhauer, Olaf, ed.), Academic Press, Oxford, pp. 156-168, 2021. [doi]
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]
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