Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints

By Qiang Du, Max D. Gunzburger, R. Lehoucq, Kun Zhou. SIAM Review, 2012

673 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mechanics of Materials, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/f98c1d475e0c3535380f94b1c187dc67fb444084

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Tadele Mengesha
2. Daniel Spector
3. Qiang Du
4. G. Em Karniadakis
5. Guofei Pang
6. Lili Ju
7. Wei Cai
8. Jesse Railo

In Mechanics of Materials

1. Tadele Mengesha
2. Daniel Spector
3. Qiang Du
4. R. Lehoucq
5. Max D. Gunzburger
6. Hao Tian
7. Lili Ju
8. Kun Zhou

In Modeling and Simulation

1. G. Em Karniadakis
2. Zhiping Mao
3. Tadele Mengesha
4. Daniel Spector
5. Jinghua Chen
6. Farzad Sabzikar
7. Qiang Du
8. Guofei Pang

Citations in the corpus

• Fractional order Orlicz-Sobolev spaces (2017, background): “Just to cite a few examples see the articles [9, 10, 12, 16, 22, 31] for some physical”
• Localization of nonlocal gradients in various topologies (2015, methodology): “Various nonlocal operators have also been used implicitly in a number of works such as [5, 6], [8, 9, 25], [13, 14], and [3], for example.”
• A conservative nonlocal convection–diffusion model and asymptotically compatible finite difference discretization (2017, methodology): “Let Ωc be an interaction domain for the specification of nonlocal boundary conditions [20].”
• TEMPERED FRACTIONAL CALCULUS (2015, background): “Even in the untempered case, many interesting open problems remain, including a rigorous proof that fractional boundary value problems are well-posed, see [19] for a nice discussion.”
• Analysis of the Volume-Constrained Peridynamic Navier Equation of Linear Elasticity (2013, background): “Previous work has focused on the well-posedness of the bond-based model introduced in [17]; see [4,11,12,15] when the deformation is vector-valued and [2,3,5,6,10, 14,16] when the deformation is scalar-valued or the related case of nonlocal diffusion.”
• Unique continuation property and Poincaré inequality for higher order fractional Laplacians with applications in inverse problems (2020, methodology): “Fractional Laplacians have a close connection to Levý processes and have been used in many areas of mathematics and physics, for example to model anomalous and nonlocal diffusion, and also in the formulation of fractional quantum mechanics where the fractional Schrödinger equation arises naturally a”
• The higher order fractional Calderón problem for linear local operators: Uniqueness (2020, background): “Fractional Laplacians appear in the study of anomalous and nonlocal diffusion, and these diffusion phenomena can be used in many areas such as continuum mechanics, graph theory and ecology just to mention a few [2, 5, 12, 27, 33].”
• What is the fractional Laplacian? A comparative review with new results (2018, methodology): “[98] proposed a type of nonlocal problem admitting a “horizon parameter”, which is used to describe an “interaction domain”, a proper subset of Rd , in which all computational considerations take place.”
• Identification of the Diffusion Parameter in Nonlocal Steady Diffusion Problems (2013, background): “In [21] (and also in [2, 4, 5]) several choices for the kernel γ are considered and analyzed.”
• Numerical methods for time-fractional evolution equations with nonsmooth data: A concise overview (2018, neutral): “nonlocal problems arising in peridynamics [25].”