A fractional model for anomalous diffusion with increased variability: Analysis, algorithms and applications to interface problems
DOI10.1002/num.22865arXiv2101.11765WikidataQ114235152 ScholiaQ114235152MaRDI QIDQ6090390
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Publication date: 16 December 2023
Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2101.11765
Smoothness and regularity of solutions to PDEs (35B65) Fractional derivatives and integrals (26A33) Dirichlet forms (31C25) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Applications of operator theory to differential and integral equations (47N20) Integral operators (45P05) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Miscellaneous topics in partial differential equations (35R99) Fractional partial differential equations (35R11) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)
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Cites Work
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- Unnamed Item
- Identification of the diffusion parameter in nonlocal steady diffusion problems
- The fractional Laplacian operator on bounded domains as a special case of the nonlocal diffusion operator
- Numerical solution for a class of nonlinear variable order fractional differential equations with Legendre wavelets
- Turbulence and diffusion. Scaling versus equations
- Wavelet solution of variable order pseudodifferential equations
- An integrodifferential model for phase transitions: stationary solutions in higher space dimensions
- Discovering variable fractional orders of advection-dispersion equations from field data using multi-fidelity Bayesian optimization
- Solution existence for non-autonomous variable-order fractional differential equations
- A fully coupled porous flow and geomechanics model for fluid driven cracks: a peridynamics approach
- Data-driven learning of nonlocal physics from high-fidelity synthetic data
- Bilevel parameter learning for nonlocal image denoising models
- nPINNs: nonlocal physics-informed neural networks for a parametrized nonlocal universal Laplacian operator. Algorithms and applications
- An energy-based coupling approach to nonlocal interface problems
- Aspects of an adaptive finite element method for the fractional Laplacian: a priori and a posteriori error estimates, efficient implementation and multigrid solver
- Regularity analyses and approximation of nonlocal variational equality and inequality problems
- The Dirichlet problem for nonlocal operators
- Peridynamics and material interfaces
- Nonlocal convection-diffusion volume-constrained problems and jump processes
- How to approximate the heat equation with Neumann boundary conditions by nonlocal diffusion problems
- Inverting the variable fractional order in a variable-order space-fractional diffusion equation with variable diffusivity: analysis and simulation
- Lower bounded semi-Dirichlet forms associated with Lévy type operators
- Wellposedness and regularity of a variable-order space-time fractional diffusion equation
- A Generalized Spectral Collocation Method with Tunable Accuracy for Variable-Order Fractional Differential Equations
- Numerical Methods for the Variable-Order Fractional Advection-Diffusion Equation with a Nonlinear Source Term
- Towards an Efficient Finite Element Method for the Integral Fractional Laplacian on Polygonal Domains
- Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints
- A NONLOCAL VECTOR CALCULUS, NONLOCAL VOLUME-CONSTRAINED PROBLEMS, AND NONLOCAL BALANCE LAWS
- Fractional Calculus: Integral and Differential Equations of Fractional Order
- A Physically Consistent, Flexible, and Efficient Strategy to Convert Local Boundary Conditions into Nonlocal Volume Constraints
- A cookbook for approximating Euclidean balls and for quadrature rules in finite element methods for nonlocal problems
- An Optimal-Order Numerical Approximation to Variable-order Space-fractional Diffusion Equations on Uniform or Graded Meshes
- fPINNs: Fractional Physics-Informed Neural Networks
- Sobolev Spaces with Non-Muckenhoupt Weights, Fractional Elliptic Operators, and Applications
- A Priori Error Estimates for the Optimal Control of the Integral Fractional Laplacian
- MHD Turbulence: Nonlocal, Anisotropic, Nonuniversal?
- The Mathematical Theory of Finite Element Methods
- Numerical methods for nonlocal and fractional models
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