Project description
Low-regularity and high oscillations: computation of dispersive equations (LAHACODE)
Partial differential equations (PDEs) play a central role in mathematics, allowing us to describe physical phenomena ranging from ultra-cold atoms up to ultra-hot matter, from learning algorithms to fluids in the human brain. To understand nature we have to understand their qualitative behavior and compute reliably their numerical approximation. While linear problems and smooth solutions are nowadays well understood, a reliable description of ‘non-smooth’ phenomena remains a challenging open problem. The overall ambition of the ERC-funded project LAHACODE is to make a crucial step towards closing this gap by deeply embedding the underlying structure of resonances into the numerical discretisation. This will allow us to link the finite dimensional discretisation to powerful existence results for nonlinear PDEs at low regularity.
Objective
Partial differential equations (PDEs) play a central role in mathematics, allowing us to describe physical phenomena ranging from ultra-cold atoms (Bose–Einstein condensation) up to ultra-hot matter (nuclear fusion), from learning algorithms to fluids in the human brain. To understand nature we have to understand their qualitative behavior: existence and long time behavior of solutions, their geometric and dynamical properties – as well as to compute reliably their numerical solution. While linear problems and smooth solutions are nowadays well understood, a reliable description of ‘non-smooth’ phenomena remains one of the most challenging open problems in computational mathematics since the underlying PDEs have very complicated solutions exhibiting high oscillations and loss of regularity. This leads to huge errors, massive computational costs and ultimately provokes the failure of classical schemes. Nevertheless, ‘non-smooth phenomena’ play a fundamental role in modern physical modeling (e.g. blow-up phenomena, turbulences, high frequencies, low dispersion limits, etc.) which makes it an essential task to develop suitable numerical schemes. The overall ambition of LAHACODE is to make a crucial step towards closing this gap – addressing the fundamental question: How and to what extent can we reproduce the qualitative behavior of differential equations in a finite (discretized) world? LAHACODE is situated at the challenging frontiers of analysis and numerics. The main objective is to develop a novel class of numerical schemes for nonlinear PDEs with strong geometric structure at low regularity and high oscillations. The key idea in the construction of the new schemes is to tackle and deeply embed the underlying structure of resonances in the numerical discretizations. As in the continuous case, these terms are central to structure preservation, and provide the new schemes with remarkable properties – allowing reliable approximations where classical schemes fail.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences mathematics pure mathematics mathematical analysis differential equations partial differential equations
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Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC)
MAIN PROGRAMME
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Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
ERC-STG - Starting Grant
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Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) ERC-2019-STG
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Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
75006 PARIS
France
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.