Modelling and Computation of Shocks and Interfaces

Leistungen

List of Summer - Winter Schools/Invited lecture series/Transferable skills activities

Report of ESRs secondments

Report on the scientific results related to Measure Valued Solutions and Uncertainty Quantification and in particular in connection to -- Construction, analysis and assessment of computational methods for measure valued solutions. -- Convergence, scalability to realistic problems, and computational efficiency of Uncertainty Quantification for HCD-PDEs. Analytical issues for stochastic HCD-PDEs. The report will include references to related papers, preprints and PhD theses.

Progress on Research Theme 4

Progress report on RT4 : Report on the scientific progress related to Applications and in particular in connection to Modeling, computation and analysis for problems in Aerodynamics (compressible Euler and Navier-Stokes equations), Geophysics and Environmental science, Oil and gas exploration, Materials (cavitation, fracture, shear bands and modelling the dynamics of dislocations, mechanical properties of cells). The report will include references to related papers and preprints if available.

Results on Research Theme 2

Report on the scientific results related to Propagating Interfaces and in particular in connection to -- Propagating phase boundaries and small scale dependent shock waves. Analytical and computational issues related to small scale dependent shock waves for non-convex hyperbolic systems and mixed type systems. -- Study of shock waves in hydrodynamic type systems where the dominant regularization mechanism is a small dispersion. The numerical resolution of these waves and its connection to propagating interfaces at atomistic level will be investigated. The report will include references to related papers, preprints and PhD theses.

Progress on Research Theme 3

Progress report on RT3 : Report on the scientific progress related to Models and Methods across scales and in particular in connection to -- Multiscale methods. Methods Design and analysis of adaptive methods for discretIzing HCD-PDEs -- Design, computation and analysis of coupled models across scales. Time dependent coupling and connection to hyperbolic and nearly hyperbolic PDEs. The report will include references to related papers and preprints if available.

Results on Research Theme 4

Report on the scientific results related to Applications and in particular in connection to Modeling, computation and analysis for problems in Aerodynamics (compressible Euler and Navier-Stokes equations), Geophysics and Environmental science, Oil and gas exploration, Materials (cavitation, fracture, shear bands and modelling the dynamics of dislocations, mechanical properties of cells). The report will include references to related papers, preprints and PhD theses.

Dissemination-2

List of conference participation

Progress on Research Theme 2

Progress report on RT2 : Report on the scientific progress related to Propagating Interfaces and in particular in connection to -- Propagating phase boundaries and small scale dependent shock waves. Analytical and computational issues related to small scale dependent shock waves for non-convex hyperbolic systems and mixed type systems. -- Study of shock waves in hydrodynamic type systems where the dominant regularization mechanism is a small dispersion. The numerical resolution of these waves and its connection to propagating interfaces at atomistic level will be investigated. The report will include references to related papers and preprints if available.

Results on Research Theme 3

Report on the scientific results related to Models and Methods across scales and in particular in connection to -- Multiscale methods. Methods Design and analysis of adaptive methods for discretIzing HCD-PDEs -- Design, computation and analysis of coupled models across scales. Time dependent coupling and connection to hyperbolic and nearly hyperbolic PDEs. The report will include references to related papers, preprints and PhD theses.

Progress on Research Theme 1

Progress report on RT1 : Report on the scientific progress related to Measure Valued Solutions and Uncertainty Quantification and in particular in connection to -- Construction, analysis and assessment of computational methods for measure valued solutions. -- Convergence, scalability to realistic problems, and computational efficiency of Uncertainty Quantification for HCD-PDEs. Analytical issues for stochastic HCD-PDEs. The report will include references to related papers and preprints if available.

Supervisory Board

Supervisory Board of the network. Due by month 2.

Management-1

Contract of SA

Midterm Review Meeting

Dissemination-1

Website/Preprint server

Veröffentlichungen

Cells exploit a phase transition to mechanically remodel the fibrous extracellular matrix

Autoren: Georgios Grekas, Maria Proestaki, Phoebus Rosakis, Jacob Notbohm, Charalambos Makridakis, Guruswami Ravichandran
Veröffentlicht in: Journal of The Royal Society Interface, Ausgabe 18/175, 2021, ISSN 1742-5662
Herausgeber: The Royal Society
DOI: 10.1098/rsif.2020.0823

Flow solutions of transport equations

Autoren: Sholeh Karimghasemi, Siegfried Müller, Michael Westdickenberg
Veröffentlicht in: Communications in Partial Differential Equations, Ausgabe 46/1, 2021, Seite(n) 98-134, ISSN 0360-5302
Herausgeber: Marcel Dekker Inc.
DOI: 10.1080/03605302.2020.1831018

The Optimal Convergence Rate of Monotone Schemes for Conservation Laws in the Wasserstein Distance

Autoren: Adrian M. Ruf, Espen Sande, Susanne Solem
Veröffentlicht in: Journal of Scientific Computing, Ausgabe 80/3, 2019, Seite(n) 1764-1776, ISSN 0885-7474
Herausgeber: Kluwer Academic/Plenum Publishers
DOI: 10.1007/s10915-019-00996-1

High Order Asymptotic Preserving Deferred Correction Implicit-Explicit Schemes for Kinetic Models

Autoren: Rémi Abgrall, Davide Torlo
Veröffentlicht in: SIAM Journal on Scientific Computing, Ausgabe 42/3, 2020, Seite(n) B816-B845, ISSN 1064-8275
Herausgeber: Society for Industrial and Applied Mathematics
DOI: 10.1137/19m128973x

Convergence of second-order, entropy stable methods for multi-dimensional conservation laws

Autoren: Neelabja Chatterjee, Ulrik Skre Fjordholm
Veröffentlicht in: ESAIM: Mathematical Modelling and Numerical Analysis, Ausgabe 54/4, 2020, Seite(n) 1415-1428, ISSN 0764-583X
Herausgeber: EDP Sciences
DOI: 10.1051/m2an/2019090

Numerical investigations into a model of partially incompressible two-phase flow in pipes

Autoren: Nils Henrik Risebro, Adrian M. Ruf
Veröffentlicht in: SeMA Journal, Ausgabe 77/2, 2020, Seite(n) 143-159, ISSN 2254-3902
Herausgeber: Springer
DOI: 10.1007/s40324-019-00207-9

Derivation of a Linearised Elasticity Model from Singularly Perturbed Multiwell Energy Functionals

Autoren: Roberto Alicandro, Gianni Dal Maso, Giuliano Lazzaroni, Mariapia Palombaro
Veröffentlicht in: Archive for Rational Mechanics and Analysis, Ausgabe 230/1, 2018, Seite(n) 1-45, ISSN 0003-9527
Herausgeber: Springer Verlag
DOI: 10.1007/s00205-018-1240-6

A new class of entropy stable schemes for hyperbolic systems: Finite element methods

Autoren: Ioannis Gkanis, Charalambos G. Makridakis
Veröffentlicht in: Mathematics of Computation, 2021, Seite(n) 1, ISSN 0025-5718
Herausgeber: American Mathematical Society
DOI: 10.1090/mcom/3617

Models for Dense Multilane Vehicular Traffic

Autoren: Helge Holden, Nils Henrik Risebro
Veröffentlicht in: SIAM Journal on Mathematical Analysis, Ausgabe 51/5, 2019, Seite(n) 3694-3713, ISSN 0036-1410
Herausgeber: Society for Industrial and Applied Mathematics
DOI: 10.1137/19m124318x

Formulation and convergence of the finite volume method for conservation laws on spacetimes with boundary

Autoren: Jan Giesselmann, Philippe G. LeFloch
Veröffentlicht in: Numerische Mathematik, Ausgabe 144/4, 2020, Seite(n) 751-785, ISSN 0029-599X
Herausgeber: Springer Verlag
DOI: 10.1007/s00211-020-01101-7

The inverse-deformation approach to fracture

Autoren: Phoebus Rosakis, Timothy J. Healey, Uğur Alyanak
Veröffentlicht in: Journal of the Mechanics and Physics of Solids, Ausgabe 150, 2021, Seite(n) 104352, ISSN 0022-5096
Herausgeber: Pergamon Press Ltd.
DOI: 10.1016/j.jmps.2021.104352

An entropy satisfying two-speed relaxation system for the barotropic Euler equations: application to the numerical approximation of low Mach number flows

Autoren: François Bouchut, Christophe Chalons, Sébastien Guisset
Veröffentlicht in: Numerische Mathematik, Ausgabe 145/1, 2020, Seite(n) 35-76, ISSN 0029-599X
Herausgeber: Springer Verlag
DOI: 10.1007/s00211-020-01111-5

A robust model for rapidly varying flows over movable bottom with suspended and bedload transport: Modelling and numerical approach

Autoren: J.C. González-Aguirre, M.J. Castro, T. Morales de Luna
Veröffentlicht in: Advances in Water Resources, Ausgabe 140, 2020, Seite(n) 103575, ISSN 0309-1708
Herausgeber: Pergamon Press Ltd.
DOI: 10.1016/j.advwatres.2020.103575

Measure-valued solutions for the equations of polyconvex adiabatic thermoelasticity

Autoren: Cleopatra Christoforou, Myrto Galanopoulou, Athanasios E. Tzavaras
Veröffentlicht in: Discrete & Continuous Dynamical Systems - A, Ausgabe 39/11, 2019, Seite(n) 6175-6206, ISSN 1553-5231
Herausgeber: American Institute of Mathematical Sciences
DOI: 10.3934/dcds.2019269

Lax-Wendroff Approximate Taylor Methods with Fast and Optimized Weighted Essentially Non-oscillatory Reconstructions

Autoren: H. Carrillo, C. Parés, D. Zorío
Veröffentlicht in: Journal of Scientific Computing, Ausgabe 86/1, 2021, ISSN 0885-7474
Herausgeber: Kluwer Academic/Plenum Publishers
DOI: 10.1007/s10915-020-01380-0

Asymptotic Structure of Cosmological Burgers Flows in One and Two Space Dimensions: A Numerical Study

Autoren: Yangyang Cao
Veröffentlicht in: Communications in Computational Physics, Ausgabe 29/2, 2020, Seite(n) 472-509, ISSN 1815-2406
Herausgeber: Global Science Press
DOI: 10.4208/cicp.oa-2020-0033

Global Evolution of the U(1) Higgs Boson: Nonlinear Stability and Uniform Energy Bounds

Autoren: Shijie Dong, Philippe G. LeFloch, Zoe Wyatt
Veröffentlicht in: Annales Henri Poincaré, 2020, ISSN 1424-0637
Herausgeber: Birkhauser Verlag
DOI: 10.1007/s00023-020-00955-9

A well balanced diffuse interface method for complex nonhydrostatic free surface flows

Autoren: Elena Gaburro; Manuel J. Castro; Michael Dumbser
Veröffentlicht in: Science Direct, Ausgabe Volume 175, 15 October 2018, 2018, Seite(n) Pages 180 - 198, ISSN 0045-7930
Herausgeber: Pergamon Press Ltd.
DOI: 10.1016/j.compfluid.2018.08.013

Global well-posedness and twist-wave solutions for the inertial Qian–Sheng model of liquid crystals

Autoren: Francesco De Anna, Arghir Zarnescu
Veröffentlicht in: Journal of Differential Equations, Ausgabe 264/2, 2018, Seite(n) 1080-1118, ISSN 0022-0396
Herausgeber: Academic Press
DOI: 10.1016/j.jde.2017.09.031

Convergence of a full discretization for a second-order nonlinear elastodynamic equation in isotropic and anisotropic Orlicz spaces

Autoren: A. M. Ruf
Veröffentlicht in: Zeitschrift für angewandte Mathematik und Physik, Ausgabe 68/5, 2017, ISSN 0044-2275
Herausgeber: Birkhauser Verlag
DOI: 10.1007/s00033-017-0863-z

Well-balanced Arbitrary-Lagrangian-Eulerian finite volume schemes on moving nonconforming meshes for the Euler equations of gas dynamics with gravity

Autoren: Elena Gaburro, Manuel J Castro, Michael Dumbser
Veröffentlicht in: Monthly Notices of the Royal Astronomical Society, Ausgabe 477/2, 2018, Seite(n) 2251-2275, ISSN 0035-8711
Herausgeber: Blackwell Publishing Inc.
DOI: 10.1093/mnras/sty542

Convergence of the finite volume method on a Schwarzschild background

Autoren: Shijie Dong, Philippe G. LeFloch
Veröffentlicht in: ESAIM: Mathematical Modelling and Numerical Analysis, Ausgabe 53/5, 2019, Seite(n) 1459-1476, ISSN 0764-583X
Herausgeber: EDP Sciences
DOI: 10.1051/m2an/2019037

Compact Approximate Taylor Methods for Systems of Conservation Laws

Autoren: H. Carrillo, C. Parés
Veröffentlicht in: Journal of Scientific Computing, Ausgabe 80/3, 2019, Seite(n) 1832-1866, ISSN 0885-7474
Herausgeber: Kluwer Academic/Plenum Publishers
DOI: 10.1007/s10915-019-01005-1

Linearly implicit all Mach number shock capturing schemes for the Euler equations

Autoren: Stavros Avgerinos, Florian Bernard, Angelo Iollo, Giovanni Russo
Veröffentlicht in: Journal of Computational Physics, Ausgabe 393, 2019, Seite(n) 278-312, ISSN 0021-9991
Herausgeber: Academic Press
DOI: 10.1016/j.jcp.2019.04.020

Well-posedness of the Initial Value Problem for the Ostrovsky–Hunter Equation with Spatially Dependent Flux

Autoren: G. M. Coclite, N. Chatterjee, N. H. Risebro
Veröffentlicht in: Milan Journal of Mathematics, Ausgabe 87/2, 2019, Seite(n) 283-301, ISSN 1424-9286
Herausgeber: Birkhauser Verlag
DOI: 10.1007/s00032-019-00302-6

Stability of a coupled wave-Klein-Gordon system with quadratic nonlinearities

Autoren: Shijie Dong, Zoe Wyatt
Veröffentlicht in: Journal of Differential Equations, Ausgabe 269/9, 2020, Seite(n) 7470-7497, ISSN 0022-0396
Herausgeber: Academic Press
DOI: 10.1016/j.jde.2020.05.019

Reprint of: Direct Arbitrary-Lagrangian-Eulerian finite volume schemes on moving nonconforming unstructured meshes

Autoren: Elena Gaburro, Michael Dumbser, Manuel J. Castro
Veröffentlicht in: Computers & Fluids, Ausgabe 169, 2018, Seite(n) 263-284, ISSN 0045-7930
Herausgeber: Pergamon Press Ltd.
DOI: 10.1016/j.compfluid.2018.03.051

A symmetrizable extension of polyconvex thermoelasticity and applications to zero-viscosity limits and weak-strong uniqueness

Autoren: Cleopatra Christoforou, Myrto Galanopoulou, Athanasios E. Tzavaras
Veröffentlicht in: Communications in Partial Differential Equations, Ausgabe 43/7, 2018, Seite(n) 1019-1050, ISSN 0360-5302
Herausgeber: Marcel Dekker Inc.
DOI: 10.1080/03605302.2018.1456551

Weak solution of the merged mathematical equations of the polluted atmosphere

Autoren: Donatella Donatelli, Nóra Juhász
Veröffentlicht in: Mathematical Methods in the Applied Sciences, Ausgabe 43/15, 2020, Seite(n) 9245-9261, ISSN 0170-4214
Herausgeber: John Wiley & Sons Inc.
DOI: 10.1002/mma.6618

Weak dissipative solutions to a free-boundary problem for finitely extensible bead-spring chain molecules: Variable viscosity coefficients

Autoren: Donatella Donatelli, Tessa Thorsen, Konstantina Trivisa
Veröffentlicht in: Kinetic & Related Models, Ausgabe 13/5, 2020, Seite(n) 1047-1070, ISSN 1937-5077
Herausgeber: American Institute of Mathematical Sciences
DOI: 10.3934/krm.2020037

All Mach Number Second Order Semi-implicit Scheme for the Euler Equations of Gas Dynamics

Autoren: S. Boscarino, G. Russo, L. Scandurra
Veröffentlicht in: Journal of Scientific Computing, Ausgabe 77/2, 2018, Seite(n) 850-884, ISSN 0885-7474
Herausgeber: Kluwer Academic/Plenum Publishers
DOI: 10.1007/s10915-018-0731-9

A convergent finite difference scheme for the Ostrovsky--Hunter equation with Dirichlet boundary conditions

Autoren: Johanna Ridder, Adrian Montgomery Ruf
Veröffentlicht in: BIT Numerical Mathematics, Ausgabe 59, (2019), 2019, Seite(n) pages775–796, ISSN 0006-3835
Herausgeber: Springer
DOI: 10.1007/s10543-019-00746-7

A convergent finite volume method for the Kuramoto equation and related nonlocal conservation laws

Autoren: N Chatterjee, U S Fjordholm
Veröffentlicht in: IMA Journal of Numerical Analysis, Ausgabe 40/1, 2018, Seite(n) 405-421, ISSN 0272-4979
Herausgeber: Oxford University Press
DOI: 10.1093/imanum/dry074

Convergence Rates of Monotone Schemes for Conservation Laws with Discontinuous Flux

Autoren: Jayesh Badwaik, Adrian M. Ruf
Veröffentlicht in: SIAM Journal on Numerical Analysis, Ausgabe 58/1, 2020, Seite(n) 607-629, ISSN 0036-1429
Herausgeber: Society for Industrial and Applied Mathematics
DOI: 10.1137/19M1283276

On a free boundary problem for finitely extensible bead-spring chain molecules in dilute polymers

Autoren: Donatella Donatelli, Konstantina Trivisa
Veröffentlicht in: Journal of Mathematical Analysis and Applications, Ausgabe 482/1, 2020, Seite(n) 123527, ISSN 0022-247X
Herausgeber: Academic Press
DOI: 10.1016/j.jmaa.2019.123527

Stability of Quasilinear Waves in $$1+1$$1+1 Dimension Under Null Condition

Autoren: Shijie Dong
Veröffentlicht in: Journal of Dynamics and Differential Equations, 2020, ISSN 1040-7294
Herausgeber: Plenum Publishers
DOI: 10.1007/s10884-020-09842-7

Lagrangian formulation and a priori estimates for relativistic fluid flows with vacuum

Autoren: Juhi Jang, Philippe G. LeFloch, Nader Masmoudi
Veröffentlicht in: Journal of Differential Equations, Ausgabe 260/6, 2016, Seite(n) 5481-5509, ISSN 0022-0396
Herausgeber: Academic Press
DOI: 10.1016/j.jde.2015.12.004

Gaussian wave packet transform based numerical scheme for the semi-classical Schrödinger equation with random inputs

Autoren: Shi Jin, Liu Liu, Giovanni Russo, Zhennan Zhou
Veröffentlicht in: Journal of Computational Physics, Ausgabe 401, 2020, Seite(n) 109015, ISSN 0021-9991
Herausgeber: Academic Press
DOI: 10.1016/j.jcp.2019.109015

Mathematics of computational modelling: some challenges of computing nonlinear phenomena

Autoren: I. Gkanis, G. Grekas, E. Karnessis & C. Makridakis
Veröffentlicht in: First Congress of Greek Mathematicians - Proceedings of the Congress held in Athens, Greece, June 25–30, 2018, 2020, Seite(n) 139-166, ISBN 9783110663075
Herausgeber: De Gruyter
DOI: 10.1515/9783110663075-007

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