Discretization and adaptive approximation of fully nonlinear equations

Project Information

DAFNE

Grant agreement ID: 891734

DOI

10.3030/891734

EC signature date 22 October 2020

Start date 1 July 2021

End date 30 June 2026

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 453 937,00

EU contribution

€ 1 453 937,00

Coordinated by

FRIEDRICH-SCHILLER-UNIVERSITÄT JENA
Germany

CORDIS provides links to public deliverables and publications of HORIZON projects.

Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Publications

Peer reviewed articles (19)

A posteriori error estimates for nonconforming discretizations of singularly perturbed biharmonic operators

Author(s): Dietmar Gallistl, Shudan Tian
Published in: The SMAI Journal of computational mathematics, Issue 10, 2025, Page(s) 355-372, ISSN 2426-8399
Publisher: MathDoc/Centre Mersenne
DOI: 10.5802/smai-jcm.115

Mixed finite elements for the Gross–Pitaevskii eigenvalue problem: <i>a priori</i> error analysis and guaranteed lower energy bound

Author(s): Dietmar Gallistl, Moritz Hauck, Yizhou Liang, Daniel Peterseim
Published in: IMA Journal of Numerical Analysis, Issue 45, 2025, Page(s) 1320-1346, ISSN 0272-4979
Publisher: Oxford University Press
DOI: 10.1093/imanum/drae048

Computational Multiscale Methods for Nondivergence-Form Elliptic Partial Differential Equations

Author(s): Philip Freese; Dietmar Gallistl; Daniel Peterseim; Timo Sprekeler
Published in: Comput. Methods Appl. Math., 2023, ISSN 1609-4840
Publisher: Walter de Gruyter and Co.
DOI: 10.1515/cmam-2023-0040

Discrete Weak Duality of Hybrid High-Order Methods for Convex Minimization Problems

Author(s): Ngoc Tien Tran
Published in: SIAM Journal on Numerical Analysis, Issue 62, 2024, Page(s) 1492-1514, ISSN 0036-1429
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/23m1594534

Minimal residual discretization of a class of fully nonlinear elliptic PDE

Author(s): Dietmar Gallistl, Ngoc Tien Tran
Published in: IMA Journal of Numerical Analysis, 2025, ISSN 0272-4979
Publisher: Oxford University Press
DOI: 10.1093/imanum/draf075

Stability and guaranteed error control of approximations to the Monge--Amp\`ere equation

Author(s): Gallistl, Dietmar; Tran, Ngoc Tien
Published in: Numer. Math., 2023, ISSN 0029-599X
Publisher: Springer Verlag
DOI: 10.1007/s00211-023-01385-5

Multiscale Sub-grid Correction Method for Time-Harmonic High-Frequency Elastodynamics with Wave Number Explicit Bounds

Author(s): Donald L. Brown; Dietmar Gallistl
Published in: Comput. Methods Appl. Math., Issue 2, 2023, ISSN 1609-4840
Publisher: Walter de Gruyter and Co.
DOI: 10.1515/cmam-2022-0041

Adaptive hybrid high-order method for guaranteed lower eigenvalue bounds

Author(s): Carsten Carstensen, Benedikt Gräßle, Ngoc Tien Tran
Published in: Numerische Mathematik, Issue 156, 2024, Page(s) 813-851, ISSN 0029-599X
Publisher: Springer Verlag
DOI: 10.1007/s00211-024-01407-w

Finite element approximation for uniformly elliptic linear PDE of second order in nondivergence form

Author(s): Ngoc Tien Tran
Published in: Mathematics of Computation, 2024, ISSN 0025-5718
Publisher: American Mathematical Society
DOI: 10.1090/mcom/3966

Continuous finite elements satisfying a strong discrete Miranda–Talenti identity

Author(s): Dietmar Gallistl, Shudan Tian
Published in: IMA Journal of Numerical Analysis, Issue 45, 2025, Page(s) 1347-1371, ISSN 0272-4979
Publisher: Oxford University Press
DOI: 10.1093/imanum/drae049

The Adini finite element on locally refined meshes

Author(s): D. Gallistl
Published in: Mathematics of Computation, 2025, ISSN 0025-5718
Publisher: American Mathematical Society
DOI: 10.1090/mcom/4117

Localized Implicit Time Stepping for the Wave Equation

Author(s): Dietmar Gallistl, Roland Maier
Published in: SIAM Journal on Numerical Analysis, Issue 62, 2024, Page(s) 1589-1608, ISSN 0036-1429
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/23m1582618

Convergence of a regularized finite element discretization of the two-dimensional Monge-Ampère equation

Author(s): Dietmar Gallistl and Ngoc Tien Tran
Published in: Mathematics of Computation, 2023, ISSN 1088-6842
Publisher: AMS
DOI: 10.1090/mcom/3794

Comparison of Guaranteed Lower Eigenvaluebounds with Three Skeletal Schemes

Author(s): Carsten Carstensen, benedikt GRAeSSLE, emilie pirch
Published in: Comput. Methods Appl. Mech. Eng., 2024, ISSN 0045-7825
Publisher: Elsevier BV
DOI: 10.2139/ssrn.4952221

Convergent adaptive hybrid higher-order schemes for convex minimization

Author(s): Carsten Carstensen, Ngoc Tien Tran
Published in: Numerische Mathematik, Issue 151, 2022, Page(s) 329-367, ISSN 0029-599X
Publisher: Springer Verlag
DOI: 10.1007/s00211-022-01284-1

Mixed methods and lower eigenvalue bounds

Author(s): Dietmar Gallistl
Published in: Math. Comp., Issue 92, 2023, Page(s) 1491-1509, ISSN 0025-5718
Publisher: American Mathematical Society
DOI: 10.1090/mcom/3820

Stabilization-free HHO a posteriori error control

Author(s): Fleurianne Bertrand; Carsten Carstensen; Benedikt Gräßle; Ngoc Tien Tran
Published in: Numer. Math., Issue 154, 2023, Page(s) 369-408, ISSN 0029-599X
Publisher: Springer Verlag
DOI: 10.1007/s00211-023-01366-8

Computational Lower Bounds of the Maxwell Eigenvalues

Author(s): Dietmar Gallistl; Vladislav Olkhovskiy
Published in: SIAM J. Numer. Anal, Issue 61, 2023, Page(s) 539-561, ISSN 0036-1429
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/21m1461447

Residual-based <i>a posteriori</i> error analysis of a Taylor–Hood discretization of the Reissner–Mindlin plate

Author(s): Dietmar Gallistl, Mira Schedensack
Published in: ESAIM: Mathematical Modelling and Numerical Analysis, Issue 59, 2025, Page(s) 2005-2019, ISSN 2822-7840
Publisher: EDP Sciences
DOI: 10.1051/m2an/2025047

Other (4)

"A Strengthened Alexandrov Maximum Principle or Uniform H\""older Continuity for Solutions of the Monge--Amp\`ere Equation with Bounded Right-Hand Side"

Author(s): Gehring, Lukas
Published in: arXiv e-prints, 2022
Publisher: arXiv

Mixed finite element approximation for non-divergence form elliptic equations with random input data

Author(s): Amireh Mousavi
Published in: 2025
Publisher: arXiv
DOI: 10.48550/arxiv.2512.04003

A Strengthened Alexandrov Maximum Principle or Uniform Hölder Continuity for Solutions of the Monge--Ampère Equation with Bounded Right-Hand Side

Author(s): Gehring, Lukas
Published in: Issue 1, 2025
Publisher: arXiv
DOI: 10.48550/arxiv.2211.01175

Adaptive Mesh Refinement for arbitrary initial Triangulations

Author(s): Diening, Lars; Gehring, Lukas; Storn, Johannes
Published in: arXiv e-prints, 2023
Publisher: arXiv
DOI: 10.48550/arxiv.2306.02674

Thesis and dissertations (1)

Te Constant in the Theorem of Binev-Dahmen-DeVore-Stevenson and a Generalisation of it

Author(s): Lukas Gehring
Published in: 2020
Publisher: arXiv e-prints