Modelling and Computation of Shocks and Interfaces

Rezultaty

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

Publikacje

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

Autorzy: Georgios Grekas, Maria Proestaki, Phoebus Rosakis, Jacob Notbohm, Charalambos Makridakis, Guruswami Ravichandran
Opublikowane w: Journal of The Royal Society Interface, Numer 18/175, 2021, ISSN 1742-5662
Wydawca: The Royal Society
DOI: 10.1098/rsif.2020.0823

Flow solutions of transport equations

Autorzy: Sholeh Karimghasemi, Siegfried Müller, Michael Westdickenberg
Opublikowane w: Communications in Partial Differential Equations, Numer 46/1, 2021, Strona(/y) 98-134, ISSN 0360-5302
Wydawca: Marcel Dekker Inc.
DOI: 10.1080/03605302.2020.1831018

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

Autorzy: Adrian M. Ruf, Espen Sande, Susanne Solem
Opublikowane w: Journal of Scientific Computing, Numer 80/3, 2019, Strona(/y) 1764-1776, ISSN 0885-7474
Wydawca: Kluwer Academic/Plenum Publishers
DOI: 10.1007/s10915-019-00996-1

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

Autorzy: Rémi Abgrall, Davide Torlo
Opublikowane w: SIAM Journal on Scientific Computing, Numer 42/3, 2020, Strona(/y) B816-B845, ISSN 1064-8275
Wydawca: Society for Industrial and Applied Mathematics
DOI: 10.1137/19m128973x

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

Autorzy: Neelabja Chatterjee, Ulrik Skre Fjordholm
Opublikowane w: ESAIM: Mathematical Modelling and Numerical Analysis, Numer 54/4, 2020, Strona(/y) 1415-1428, ISSN 0764-583X
Wydawca: EDP Sciences
DOI: 10.1051/m2an/2019090

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

Autorzy: Nils Henrik Risebro, Adrian M. Ruf
Opublikowane w: SeMA Journal, Numer 77/2, 2020, Strona(/y) 143-159, ISSN 2254-3902
Wydawca: Springer
DOI: 10.1007/s40324-019-00207-9

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

Autorzy: Roberto Alicandro, Gianni Dal Maso, Giuliano Lazzaroni, Mariapia Palombaro
Opublikowane w: Archive for Rational Mechanics and Analysis, Numer 230/1, 2018, Strona(/y) 1-45, ISSN 0003-9527
Wydawca: Springer Verlag
DOI: 10.1007/s00205-018-1240-6

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

Autorzy: Ioannis Gkanis, Charalambos G. Makridakis
Opublikowane w: Mathematics of Computation, 2021, Strona(/y) 1, ISSN 0025-5718
Wydawca: American Mathematical Society
DOI: 10.1090/mcom/3617

Models for Dense Multilane Vehicular Traffic

Autorzy: Helge Holden, Nils Henrik Risebro
Opublikowane w: SIAM Journal on Mathematical Analysis, Numer 51/5, 2019, Strona(/y) 3694-3713, ISSN 0036-1410
Wydawca: 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

Autorzy: Jan Giesselmann, Philippe G. LeFloch
Opublikowane w: Numerische Mathematik, Numer 144/4, 2020, Strona(/y) 751-785, ISSN 0029-599X
Wydawca: Springer Verlag
DOI: 10.1007/s00211-020-01101-7

The inverse-deformation approach to fracture

Autorzy: Phoebus Rosakis, Timothy J. Healey, Uğur Alyanak
Opublikowane w: Journal of the Mechanics and Physics of Solids, Numer 150, 2021, Strona(/y) 104352, ISSN 0022-5096
Wydawca: 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

Autorzy: François Bouchut, Christophe Chalons, Sébastien Guisset
Opublikowane w: Numerische Mathematik, Numer 145/1, 2020, Strona(/y) 35-76, ISSN 0029-599X
Wydawca: 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

Autorzy: J.C. González-Aguirre, M.J. Castro, T. Morales de Luna
Opublikowane w: Advances in Water Resources, Numer 140, 2020, Strona(/y) 103575, ISSN 0309-1708
Wydawca: Pergamon Press Ltd.
DOI: 10.1016/j.advwatres.2020.103575

Measure-valued solutions for the equations of polyconvex adiabatic thermoelasticity

Autorzy: Cleopatra Christoforou, Myrto Galanopoulou, Athanasios E. Tzavaras
Opublikowane w: Discrete & Continuous Dynamical Systems - A, Numer 39/11, 2019, Strona(/y) 6175-6206, ISSN 1553-5231
Wydawca: American Institute of Mathematical Sciences
DOI: 10.3934/dcds.2019269

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

Autorzy: H. Carrillo, C. Parés, D. Zorío
Opublikowane w: Journal of Scientific Computing, Numer 86/1, 2021, ISSN 0885-7474
Wydawca: 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

Autorzy: Yangyang Cao
Opublikowane w: Communications in Computational Physics, Numer 29/2, 2020, Strona(/y) 472-509, ISSN 1815-2406
Wydawca: Global Science Press
DOI: 10.4208/cicp.oa-2020-0033

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

Autorzy: Shijie Dong, Philippe G. LeFloch, Zoe Wyatt
Opublikowane w: Annales Henri Poincaré, 2020, ISSN 1424-0637
Wydawca: Birkhauser Verlag
DOI: 10.1007/s00023-020-00955-9

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

Autorzy: Elena Gaburro; Manuel J. Castro; Michael Dumbser
Opublikowane w: Science Direct, Numer Volume 175, 15 October 2018, 2018, Strona(/y) Pages 180 - 198, ISSN 0045-7930
Wydawca: 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

Autorzy: Francesco De Anna, Arghir Zarnescu
Opublikowane w: Journal of Differential Equations, Numer 264/2, 2018, Strona(/y) 1080-1118, ISSN 0022-0396
Wydawca: 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

Autorzy: A. M. Ruf
Opublikowane w: Zeitschrift für angewandte Mathematik und Physik, Numer 68/5, 2017, ISSN 0044-2275
Wydawca: 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

Autorzy: Elena Gaburro, Manuel J Castro, Michael Dumbser
Opublikowane w: Monthly Notices of the Royal Astronomical Society, Numer 477/2, 2018, Strona(/y) 2251-2275, ISSN 0035-8711
Wydawca: Blackwell Publishing Inc.
DOI: 10.1093/mnras/sty542

Convergence of the finite volume method on a Schwarzschild background

Autorzy: Shijie Dong, Philippe G. LeFloch
Opublikowane w: ESAIM: Mathematical Modelling and Numerical Analysis, Numer 53/5, 2019, Strona(/y) 1459-1476, ISSN 0764-583X
Wydawca: EDP Sciences
DOI: 10.1051/m2an/2019037

Compact Approximate Taylor Methods for Systems of Conservation Laws

Autorzy: H. Carrillo, C. Parés
Opublikowane w: Journal of Scientific Computing, Numer 80/3, 2019, Strona(/y) 1832-1866, ISSN 0885-7474
Wydawca: Kluwer Academic/Plenum Publishers
DOI: 10.1007/s10915-019-01005-1

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

Autorzy: Stavros Avgerinos, Florian Bernard, Angelo Iollo, Giovanni Russo
Opublikowane w: Journal of Computational Physics, Numer 393, 2019, Strona(/y) 278-312, ISSN 0021-9991
Wydawca: 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

Autorzy: G. M. Coclite, N. Chatterjee, N. H. Risebro
Opublikowane w: Milan Journal of Mathematics, Numer 87/2, 2019, Strona(/y) 283-301, ISSN 1424-9286
Wydawca: Birkhauser Verlag
DOI: 10.1007/s00032-019-00302-6

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

Autorzy: Shijie Dong, Zoe Wyatt
Opublikowane w: Journal of Differential Equations, Numer 269/9, 2020, Strona(/y) 7470-7497, ISSN 0022-0396
Wydawca: Academic Press
DOI: 10.1016/j.jde.2020.05.019

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

Autorzy: Elena Gaburro, Michael Dumbser, Manuel J. Castro
Opublikowane w: Computers & Fluids, Numer 169, 2018, Strona(/y) 263-284, ISSN 0045-7930
Wydawca: 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

Autorzy: Cleopatra Christoforou, Myrto Galanopoulou, Athanasios E. Tzavaras
Opublikowane w: Communications in Partial Differential Equations, Numer 43/7, 2018, Strona(/y) 1019-1050, ISSN 0360-5302
Wydawca: Marcel Dekker Inc.
DOI: 10.1080/03605302.2018.1456551

Weak solution of the merged mathematical equations of the polluted atmosphere

Autorzy: Donatella Donatelli, Nóra Juhász
Opublikowane w: Mathematical Methods in the Applied Sciences, Numer 43/15, 2020, Strona(/y) 9245-9261, ISSN 0170-4214
Wydawca: 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

Autorzy: Donatella Donatelli, Tessa Thorsen, Konstantina Trivisa
Opublikowane w: Kinetic & Related Models, Numer 13/5, 2020, Strona(/y) 1047-1070, ISSN 1937-5077
Wydawca: 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

Autorzy: S. Boscarino, G. Russo, L. Scandurra
Opublikowane w: Journal of Scientific Computing, Numer 77/2, 2018, Strona(/y) 850-884, ISSN 0885-7474
Wydawca: 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

Autorzy: Johanna Ridder, Adrian Montgomery Ruf
Opublikowane w: BIT Numerical Mathematics, Numer 59, (2019), 2019, Strona(/y) pages775–796, ISSN 0006-3835
Wydawca: Springer
DOI: 10.1007/s10543-019-00746-7

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

Autorzy: N Chatterjee, U S Fjordholm
Opublikowane w: IMA Journal of Numerical Analysis, Numer 40/1, 2018, Strona(/y) 405-421, ISSN 0272-4979
Wydawca: Oxford University Press
DOI: 10.1093/imanum/dry074

Convergence Rates of Monotone Schemes for Conservation Laws with Discontinuous Flux

Autorzy: Jayesh Badwaik, Adrian M. Ruf
Opublikowane w: SIAM Journal on Numerical Analysis, Numer 58/1, 2020, Strona(/y) 607-629, ISSN 0036-1429
Wydawca: 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

Autorzy: Donatella Donatelli, Konstantina Trivisa
Opublikowane w: Journal of Mathematical Analysis and Applications, Numer 482/1, 2020, Strona(/y) 123527, ISSN 0022-247X
Wydawca: Academic Press
DOI: 10.1016/j.jmaa.2019.123527

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

Autorzy: Shijie Dong
Opublikowane w: Journal of Dynamics and Differential Equations, 2020, ISSN 1040-7294
Wydawca: Plenum Publishers
DOI: 10.1007/s10884-020-09842-7

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

Autorzy: Juhi Jang, Philippe G. LeFloch, Nader Masmoudi
Opublikowane w: Journal of Differential Equations, Numer 260/6, 2016, Strona(/y) 5481-5509, ISSN 0022-0396
Wydawca: 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

Autorzy: Shi Jin, Liu Liu, Giovanni Russo, Zhennan Zhou
Opublikowane w: Journal of Computational Physics, Numer 401, 2020, Strona(/y) 109015, ISSN 0021-9991
Wydawca: Academic Press
DOI: 10.1016/j.jcp.2019.109015

Mathematics of computational modelling: some challenges of computing nonlinear phenomena

Autorzy: I. Gkanis, G. Grekas, E. Karnessis & C. Makridakis
Opublikowane w: First Congress of Greek Mathematicians - Proceedings of the Congress held in Athens, Greece, June 25–30, 2018, 2020, Strona(/y) 139-166, ISBN 9783110663075
Wydawca: De Gruyter
DOI: 10.1515/9783110663075-007

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