Nonlocal gradient operators with a nonspherical interaction neighborhood and their applications
ESAIM: M2AN, 54 1 (2020) 105-128
Published online: 2020-01-14
Articles citing this article
The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
This article has been cited by the following article(s):
A stabilised peridynamic framework for modelling elastoplastic deformation and progressive failure in geomaterials
Yixin Li and Xueyu GengJournal of Rock Mechanics and Geotechnical Engineering (2025)
https://doi.org/10.1016/j.jrmge.2025.09.020
Nonlocal gradients: Fundamental theorem of calculus, Poincaré inequalities, and embeddings
José Carlos Bellido, Carlos Mora‐Corral and Hidde SchönbergerJournal of the London Mathematical Society 112 (2) (2025)
https://doi.org/10.1112/jlms.70277
Compactness results for a Dirichlet energy of nonlocal gradient with applications
Zhaolong Han, Tadele Mengesha and Xiaochuan TianNumerical Methods for Partial Differential Equations 40 (6) (2024)
https://doi.org/10.1002/num.23149
Non-local gradients in bounded domains motivated by continuum mechanics: Fundamental theorem of calculus and embeddings
José Carlos Bellido, Javier Cueto and Carlos Mora-CorralAdvances in Nonlinear Analysis 12 (1) (2023)
https://doi.org/10.1515/anona-2022-0316
Nonlocal half-ball vector operators on bounded domains: Poincaré inequality and its applications
Zhaolong Han and Xiaochuan TianMathematical Models and Methods in Applied Sciences 33 (12) 2507 (2023)
https://doi.org/10.1142/S0218202523500549
A variational theory for integral functionals involving finite-horizon fractional gradients
Javier Cueto, Carolin Kreisbeck and Hidde SchönbergerFractional Calculus and Applied Analysis 26 (5) 2001 (2023)
https://doi.org/10.1007/s13540-023-00196-7
On the solution of hyperbolic equations using the peridynamic differential operator
Ali Can Bekar, Erdogan Madenci and Ehsan HaghighatComputer Methods in Applied Mechanics and Engineering 391 114574 (2022)
https://doi.org/10.1016/j.cma.2022.114574
A new nonlocal calculus framework. Helmholtz decompositions, properties, and convergence for nonlocal operators in the limit of the vanishing horizon
Andrew Haar and Petronela RaduPartial Differential Equations and Applications 3 (3) (2022)
https://doi.org/10.1007/s42985-022-00178-z
Stability of a Nonlocal Traffic Flow Model for Connected Vehicles
Kuang Huang and Qiang DuSIAM Journal on Applied Mathematics 82 (1) 221 (2022)
https://doi.org/10.1137/20M1355732
Optimization and learning with nonlocal calculus
Sriram NagarajFoundations of Data Science 4 (3) 323 (2022)
https://doi.org/10.3934/fods.2022009
Connections between nonlocal operators: from vector calculus identities to a fractional Helmholtz decomposition
Marta D’Elia, Mamikon Gulian, Tadele Mengesha and James M. ScottFractional Calculus and Applied Analysis 25 (6) 2488 (2022)
https://doi.org/10.1007/s13540-022-00038-y
A Petrov-Galerkin method for nonlocal convection-dominated diffusion problems
Yu Leng, Xiaochuan Tian, Leszek Demkowicz, Hector Gomez and John T. FosterJournal of Computational Physics 452 110919 (2022)
https://doi.org/10.1016/j.jcp.2021.110919
Towards a Unified theory of Fractional and Nonlocal Vector Calculus
Marta D’Elia, Mamikon Gulian, Hayley Olson and George Em KarniadakisFractional Calculus and Applied Analysis 24 (5) 1301 (2021)
https://doi.org/10.1515/fca-2021-0057
Numerical methods for nonlocal and fractional models
Marta D’Elia, Qiang Du, Christian Glusa, et al.Acta Numerica 29 1 (2020)
https://doi.org/10.1017/S096249292000001X