DAFNE: Discretisation and numerical analysis of fully nonlinear equations

Preprints

1. D. Gallistl and S. Tian.
   A posteriori error estimates for nonconforming discretizations of singularly perturbed biharmonic operatorsExterner Link, arxiv:2310.15665 (2023).
2. N. T. Tran. 
   Discrete weak duality of hybrid high-order methods for convex minimization problemsExterner Link, arXiv:2308.03223 (2023)
3. D. Gallistl and R. Maier.
   Localized implicit time stepping for the wave equationExterner Link, arxiv:2306.17056 (2023)
4. L. Diening, L. Gehring, J. Storn. 
   Adaptive mesh refinement for arbitraryExterner Link
   initial triangulationsExterner Link, arxiv:2306.02674 (2023)
5. N. T. Tran. 
   Finite element approximation for uniformly elliptic linear PDE of second order inExterner Link
   nondivergence formExterner Link, arxiv.org:2302.04202 (2023)
6. D. Gallistl and N. T. Tran.
   Stability and guaranteed error control of approximations to theExterner Link
   Monge–Ampère equationExterner Link, arXiv:2301.06805 (2023)
7. L. Gehring.
   A Strengthened Alexandrov Maximum Principle or Uniform Hölder Continuity for Solutions of the Monge‒Ampère Equation with Bounded Right-Hand SideExterner Link, arXiv:2211.01175 (2022)
8. D. Gallistl and S. Tian. 
   Continuous finite elements satisfying a strong discrete Miranda–Talenti identityExterner Link arxiv:2209.12500 (2022)

Peer-reviewed works

1. F. Bertrand, C. Carstensen, B. Gräßle, and N. T. Tran.
   Stabilization-free HHO a posteriori error controlExterner Link, Numer. Math 154, pp.369–408 (2023)
2. D. Gallistl and N. T. Tran.
   Stability and guaranteed error control of approximations to the Monge–Ampère equationExterner Link, Numer. Math., (2023) (In press)
3. P. Freese, D. Gallistl, D. Peterseim and T. Sprekeler.
   Computational multiscale methods for nondivergence-form elliptic partial differential equationsExterner Link, Comput. Methods Appl. Math. (2023) (published online)
4. D. Gallistl.
   Mixed methods and lower eigenvalue boundsExterner Link, Math. Comp., volume 92, no.342, pp.1491–1509 (2023)
5. D. Gallistl and N. T. Tran.
   Convergence of a regularized finite element discretization of the two-dimensional Monge–Ampère equationExterner Link, Math. Comp., volume 92, no.342, pp.1467–1490 (2023)
6. D. Gallistl and V. Olkhovskiy.
   Computational lower bounds of the Maxwell eigenvaluesExterner Link, SIAM J. Numer. Anal., volume 61, no.2, pp.539–561 (2023)
7. D. Brown and D. Gallistl.
   Multiscale sub-grid correction method for time-harmonic high-frequency elastodynamics with wave number explicit boundsExterner Link, Comput. Methods Appl. Math., volume 23, no.1, pp.65–82 (2023)
8. K. Liu, D. Gallistl, M. Schlottbom and J. J. W. van der Vegt.
   Analysis of a mixed discontinuous Galerkin method for the time-harmonic Maxwell equations with minimal smoothness requirementsExterner Link, IMA J. Numer. Anal., volume 43, no.4, pp.2320–2351 (2023)

Talks

Ngoc Tien Tran

1. Unstabilized hybrid high-order method for a class of degenerate convex minimization problems, CC2LX Workshop on Finite Element Methods and Adaptivity, Wien, 31.03.2022
2. A hybrid high-order method for guaranteed lower eigenvalue bounds,
   WAND, Salzburg, 15.07.2022
3. Convergent adaptive hybrid higher-order schemes for convex minimization,
   NA-LaB, Berlin, 22.07.2022
4. Convergence of a regularized FE discretization of the 2D Monge–Ampère equation,
   GAMM 2022, Aachen, 16.08.2022
5. A finite element method for uniformly elliptic linear PDE of second order in nondivergence form, Berlin Workshop on Numerical Analysis 2022, Berlin, 08.11.2022
6. A regularized scheme for the Monge–Ampère equation,
   Finite Element Workshop, Jena, 20.03.2023
7. Minimal residual method for linear PDE of second order in nondivergence form,
   Finite element fair 2023, 13.05.2023
8. A regularized scheme for the Monge–Ampère equation,
   Saale-Elster-Colloquium (SEC), Halle, 25.05.2023
9. Finite element approximation for second order linear PDE in nondivergence form,
   GAMM 2023, Dresden, 01.06.2023
10. Error analysis of a skeletal method for convex minimization problems using duality relations, Jena-Augsburg-Meeting (JAM) on Numerical Analysis, 09.06.2023
11. Adaptive hybrid high-order method for guaranteed lower eigenvalue bounds,
    29th Biennial Conference on Numerical Analysis, Glasgow, 28.06.2023
12. Minimal residual methods for uniformly elliptic PDE of second order in nondivergence form, DMV-Jahrestagung 2023, Ilmenau, 27.09.2023

Dietmar Gallistl

1. Adaptive discretization of HJB equations with Cordes coefficients,
   Oberwolfach Workshop 2126b “Numerical Methods for Fully Nonlinear and Related PDEs”, 27.6.–3.7.2021 (online)
2. Adaptive discretization of HJB equations with Cordes coefficients (invited plenary),
   Chemnitz Finite Element Symposium 2021, Chemnitz, 06.-08.09.2021
3. Computational lower bounds of the Maxwell eigenvalues,
   GAMM Workshop Numerische Analysis 2021, Hannover, 27.-28.09.2021
4. A posteriori error analysis of the inf-sup constant for the divergence,
   BI.discrete21, Bielefeld, 29.09.-01.10.2021
5. Rayleigh–Ritz approximation of the inf-sup constant for the divergence, PDE & Scientific Computing Seminar, National University of Singapore, 15.10.2021 (online)
6. Rayleigh–Ritz approximation of the inf-sup constant for the divergence,
   Numerical Analysis Seminar, The University of Hong Kong, 16.2.2022 (online)
7. On the usefulness of mixed methods for eigenvalue computation,
   CC2LX - Workshop on Finite Element Methods and Adaptivity, TU Wien, 31.3.–1.4.2022
8. Convergence of a regularized finite element discretization of the two-dimensional Monge–Ampère equation, Equadiff 15, 11.-15.7.2022, Brno, Czech Republic
9. Mixed methods and lower eigenvalue bounds,
   GAMM-Jahrestagung, Aachen, 15.-19.08.2022
10. Convergence of a regularized finite element discretization of the two-dimensional Monge–Ampère equation, International Conference on Computational Partial Differential Equations and Applications (ICCPDEA-2022) 6.–8.9.2022, BML Munjal University, India (online)
11. Convergence of a regularized finite element discretization of the two-dimensional Monge–Ampère equation, DMV-Jahrestagung, Berlin, 12.-16.09.2022
12. Computational lower bounds of the Maxwell eigenvalues,
    Berlin Workshop on Numerical Analysis, Berlin, 07.11.2022
13. Mixed methods and lower eigenvalue bounds,
    The 20th European Finite Element Fair, U Twente, NL, 12.-13.05.2023
14. A posteriori error analysis of the inf-sup constant for the divergence,
    GAMM-Jahrestagung, Dresden, 30.05.-02.06.2023
15. A posteriori error control in the max morm for the Monge-Ampère equation,
    DMV-Jahrestagung, Ilmenau, 25.-28.09.2023

Emilie Pirch

1. Comparison of guaranteed lower eigenvalue bounds with three skeletal methods, International Conference on Spectral and High Order Methods (ICOSAHOM), Seoul, 14.-18.08.2023
2. Comparison of guaranteed lower eigenvalue bounds with three skeletal methods, 10th International Congress on Industrial and Applied Mathematics (ICIAM), Tokio, 20.-25.08.2023
3. Numerical experiments with three skeletal methods, Numerical methods for spectral problems: theory and applications (NMSP) 2023, Kushiro, Hokkaido, Japan, 26-31.08.2023

Lukas Gehring

1. Initial refinement is unnecessary for #Simplices <~ #Initial + #Marked in any dimension. SIAM International Meshing Roundtable (IMR), Amsterdam, 8.3.2023
2. A lower bound for the constant in the theorem of Binev‒Dahmen‒DeVore‒Stevenson, CMAM Conference, Wien, 1.9.2022
3. Initial refinement is unnecessary for #Simplices <~ #Initial + #Marked in any dimension. CC2LX - Workshop on Finite Element Methods and Adaptivity, TU Wien, 1.4.2022