Fractional vector calculus for fractional advection–dispersion
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journal
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July 2006 |
How to Approximate the Heat Equation with Neumann Boundary Conditions by Nonlocal Diffusion Problems
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November 2007 |
Multiscaling fractional advection-dispersion equations and their solutions: MULTISCALING FRACTIONAL ADES
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January 2003 |
An energy-based coupling approach to nonlocal interface problems
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July 2020 |
A FEM for an Optimal Control Problem of Fractional Powers of Elliptic Operators
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journal
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January 2015 |
Sparse Optimal Control for Fractional Diffusion
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September 2017 |
Numerical methods for nonlocal and fractional models
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journal
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May 2020 |
Mathematical and Numerical Analysis of Linear Peridynamic Models with Nonlocal Boundary Conditions
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January 2010 |
Fractional Diffusion on Bounded Domains
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January 2015 |
Uniquely identifying the variable order of time-fractional partial differential equations on general multi-dimensional domains
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November 2020 |
Identification of the Diffusion Parameter in Nonlocal Steady Diffusion Problems
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May 2015 |
Numerical solution of the heat equation with nonlocal boundary conditions
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October 1999 |
Modeling non-Fickian transport in geological formations as a continuous time random walk
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January 2006 |
Peridynamics and Material Interfaces
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January 2015 |
Affine Approximation of Parametrized Kernels and Model Order Reduction for Nonlocal and Fractional Laplace Models
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journal
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January 2020 |
A Space-Time Fractional Optimal Control Problem: Analysis and Discretization
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journal
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January 2016 |
Aspects of an adaptive finite element method for the fractional Laplacian: A priori and a posteriori error estimates, efficient implementation and multigrid solver
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December 2017 |
fPINNs: Fractional Physics-Informed Neural Networks
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January 2019 |
What is the fractional Laplacian? A comparative review with new results
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March 2020 |
Error Estimates for the Optimal Control of a Parabolic Fractional PDE
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January 2021 |
Bilevel Parameter Learning for Nonlocal Image Denoising Models
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April 2021 |
On Fractional Laplacians
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August 2014 |
Application of a fractional advection-dispersion equation
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February 2000 |
Is Gauss Quadrature Better than Clenshaw–Curtis?
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journal
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January 2008 |
Fractional Laplacians on domains, a development of Hörmander's theory of μ-transmission pseudodifferential operators
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January 2015 |
Machine Learning of Space-Fractional Differential Equations
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journal
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January 2019 |
A New Type of Identification Problems: Optimizing the Fractional Order in a Nonlocal Evolution Equation
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journal
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January 2017 |
A Physically Consistent, Flexible, and Efficient Strategy to Convert Local Boundary Conditions into Nonlocal Volume Constraints
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journal
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January 2020 |
Discovering variable fractional orders of advection–dispersion equations from field data using multi-fidelity Bayesian optimization
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November 2017 |
Stabilized linear semi-implicit schemes for the nonlocal Cahn–Hilliard equation
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June 2018 |
Perspective on theories of non-Fickian transport in heterogeneous media
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May 2009 |
A spectral Galerkin approximation of optimal control problem governed by fractional advection–diffusion–reaction equations
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April 2021 |
First passage times for symmetric stable processes in space
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January 1961 |
The Dirichlet problem for nonlocal operators
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November 2014 |
Interface problems in nonlocal diffusion and sharp transitions between local and nonlocal domains
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November 2013 |
The fractional Laplacian operator on bounded domains as a special case of the nonlocal diffusion operator
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October 2013 |
A review of applications of fractional advection–dispersion equations for anomalous solute transport in surface and subsurface water
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May 2020 |
Regularity analyses and approximation of nonlocal variational equality and inequality problems
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October 2019 |
A FEM for an optimal control problem subject to the fractional Laplace equation
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September 2019 |
A meshfree method based on the peridynamic model of solid mechanics
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journal
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June 2005 |
A direct O(Nlog2N) finite difference method for fractional diffusion equations
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October 2010 |
Optimizing the Fractional Power in a Model with Stochastic PDE Constraints
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March 2018 |
Persistence of anomalous dispersion in uniform porous media demonstrated by pore-scale simulations: ANOMALOUS DISPERSION IN UNIFORM POROUS MEDIA
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July 2007 |
A fast solver for spectral elements applied to fractional differential equations using hierarchical matrix approximation
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July 2020 |
Eulerian derivation of the fractional advection–dispersion equation
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March 2001 |
An adaptive finite element method for the sparse optimal control of fractional diffusion
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October 2019 |
Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints
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January 2012 |
A Priori Error Estimates for the Optimal Control of the Integral Fractional Laplacian
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January 2019 |
Measurement and analysis of non-Fickian dispersion in heterogeneous porous media
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journal
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July 2003 |
Asymptotically Compatible Fourier Spectral Approximations of Nonlocal Allen--Cahn Equations
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January 2016 |
A Fractional Laplace Equation: Regularity of Solutions and Finite Element Approximations
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journal
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January 2017 |
Optimization with Respect to Order in a Fractional Diffusion Model: Analysis, Approximation and Algorithmic Aspects
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journal
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March 2018 |
The fractional Laplacian operator on bounded domains as a special case of the nonlocal diffusion operator
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preprint
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January 2013 |
A new type of identification problems: optimizing the fractional order in a nonlocal evolution equation
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preprint
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January 2016 |
Aspects of an adaptive finite element method for the fractional Laplacian: a priori and a posteriori error estimates, efficient implementation and multigrid solver
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text
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January 2017 |
A priori error estimates for the optimal control of the integral fractional Laplacian
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text
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January 2018 |
Numerical methods for nonlocal and fractional models
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text
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January 2020 |
On a nonlocal Cahn-Hilliard model permitting sharp interfaces
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text
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January 2020 |