Asymptotically compatible schemes for space-time nonlocal diffusion equations

[1]  Qiang Du,et al.  Asymptotically Compatible Schemes and Applications to Robust Discretization of Nonlocal Models , 2014, SIAM J. Numer. Anal..

[2]  Jiang Yang,et al.  Asymptotically Compatible Fourier Spectral Approximations of Nonlocal Allen-Cahn Equations , 2016, SIAM J. Numer. Anal..

[3]  Marta D'Elia,et al.  The fractional Laplacian operator on bounded domains as a special case of the nonlocal diffusion operator , 2013, Comput. Math. Appl..

[4]  Qiang Du,et al.  Robust a posteriori stress analysis for quadrature collocation approximations of nonlocal models via nonlocal gradients , 2016 .

[5]  Qiang Du,et al.  Analysis and Comparison of Different Approximations to Nonlocal Diffusion and Linear Peridynamic Equations , 2013, SIAM J. Numer. Anal..

[6]  J. Pasciak,et al.  Error analysis of semidiscrete finite element methods for inhomogeneous time-fractional diffusion , 2013, 1307.1068.

[7]  Xavier Ros-Oton,et al.  The Dirichlet problem for the fractional Laplacian: Regularity up to the boundary , 2012, 1207.5985.

[8]  Qiang Du,et al.  Analysis of a nonlocal-in-time parabolic equation , 2016 .

[9]  Qiang Du,et al.  Nonlocal convection–diffusion problems and finite element approximations , 2015 .

[10]  Masahiro Yamamoto,et al.  Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems , 2011 .

[11]  X. Chen,et al.  Continuous and discontinuous finite element methods for a peridynamics model of mechanics , 2011 .

[12]  R. Lehoucq,et al.  Peridynamic Theory of Solid Mechanics , 2010 .

[13]  William McLean,et al.  Convergence analysis of a discontinuous Galerkin method for a sub-diffusion equation , 2009, Numerical Algorithms.

[14]  Raytcho D. Lazarov,et al.  Error Estimates for a Semidiscrete Finite Element Method for Fractional Order Parabolic Equations , 2012, SIAM J. Numer. Anal..

[15]  Kun Zhou,et al.  Mathematical and Numerical Analysis of Linear Peridynamic Models with Nonlocal Boundary Conditions , 2010, SIAM J. Numer. Anal..

[16]  Jean-Michel Morel,et al.  Image Denoising Methods. A New Nonlocal Principle , 2010, SIAM Rev..

[17]  Lili Ju,et al.  Quadrature rules for finite element approximations of 1D nonlocal problems , 2016, J. Comput. Phys..

[18]  Kassem Mustapha,et al.  A Discontinuous Petrov-Galerkin Method for Time-Fractional Diffusion Equations , 2014, SIAM J. Numer. Anal..

[19]  Ricardo H. Nochetto,et al.  A PDE Approach to Space-Time Fractional Parabolic Problems , 2014, SIAM J. Numer. Anal..

[20]  S. Silling.  Reformulation of Elasticity Theory for Discontinuities and Long-Range Forces , 2000 .

[21]  R. Lehoucq,et al.  Fractional Diffusion on Bounded Domains , 2015 .

[22]  M. Kwasnicki,et al.  Ten equivalent definitions of the fractional laplace operator , 2015, 1507.07356.

[23]  R. Metzler,et al.  Space- and time-fractional diffusion and wave equations, fractional Fokker-Planck equations, and physical motivation , 2002 .

[24]  Li Tian,et al.  A Convergent Adaptive Finite Element Algorithm for Nonlocal Diffusion and Peridynamic Models , 2013, SIAM J. Numer. Anal..

[25]  Guy Gilboa,et al.  Nonlocal Operators with Applications to Image Processing , 2008, Multiscale Model. Simul..

[26]  Daniel Spector,et al.  Localization of nonlocal gradients in various topologies , 2015 .

[27]  Qiang Du,et al.  Asymptotically compatible schemes for the approximation of fractional Laplacian and related nonlocal diffusion problems on bounded domains , 2016, Adv. Comput. Math..

[28]  Florin Bobaru,et al.  The peridynamic formulation for transient heat conduction , 2010 .

[29]  Bangti Jin,et al.  Two Fully Discrete Schemes for Fractional Diffusion and Diffusion-Wave Equations with Nonsmooth Data , 2016, SIAM J. Sci. Comput..

[30]  Hong Wang,et al.  A fast Galerkin method with efficient matrix assembly and storage for a peridynamic model , 2012, J. Comput. Phys..

[31]  Mikhail Belkin,et al.  On Learning with Integral Operators , 2010, J. Mach. Learn. Res..

[32]  Kun Zhou,et al.  Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints , 2012, SIAM Rev..