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1. | Department of Scientific Computing, Florida State University, Tallahassee, FL 32306, United States, United States |
References:
[1] |
B. Aksoylu and T. Mengesha, Results on nonlocal boundary value problems, Numer. Funct. Anal. Optim., 31 (2010), 1301-1317.
doi: 10.1080/01630563.2010.519136. |
[2] |
A. Buades, B. Coll and J. Morel, Image denoising methods: A new nonlocal principle, SIAM Review, 52 (2010), 113-147.
doi: 10.1137/090773908. |
[3] |
X. Chen and M. Gunzburger, Continuous and discontinuous finite element methods for a peridynamics model of mechanics, Comput. Meth. Appl. Mech. Engrg., 200 (2011), 1237-1250.
doi: 10.1016/j.cma.2010.10.014. |
[4] |
Q. Du, M. Gunzburger, R. Lehoucq and K. Zhou, Analysis and approximation of nonlocal diffusion problems with volume constraints, SIAM Review, 54 (2012), 667-696.
doi: 10.1137/110833294. |
[5] |
Q. Du, L. Tian and X. Zhao, A Convergent Adaptive Finite Element Algorithm for Nonlocal Diffusion and Peridynamic Models, SIAM J. Numer. Anal., 51 (2013), 1211-1234.
doi: 10.1137/120871638. |
[6] |
V. Ervin, N. Heuer and J. Roop, Numerical approximation of a time dependent, non-linear, fractional order diffusion equation, SIAM J. Math. Anal., 45 (2007), 572-591.
doi: 10.1137/050642757. |
[7] |
G. Gilboa and S. Osher, Nonlocal linear image regularization and supervised segmentation, Multiscale Model. Simul., 6 (2007), 595-630.
doi: 10.1137/060669358. |
[8] |
G. Gilboa and S. Osher, Nonlocal operators with applications to image processing, Multiscale Model. Simul., 7 (2008), 1005-1028.
doi: 10.1137/070698592. |
[9] |
M. Gunzburger and R. Lehoucq, A nonlocal vector calculus with application to nonlocal boundary value problems, Multiscale Model. Simul., 8 (2010), 1581-1598.
doi: 10.1137/090766607. |
[10] |
Y. Lou, X. Zhang, S. Osher and A. Bertozzi, Image recovery via nonlocal operators, J. Sci. Comput., 42 (2010), 185-197.
doi: 10.1007/s10915-009-9320-2. |
[11] |
H. Wang and H. Tian, A fast Galerkin method with efficient matrix assembly and storage for a peridynamic model, J. Comput. Phys., 231 (2012), 7730-7738.
doi: 10.1016/j.jcp.2012.06.009. |
[12] |
O. Weckner and R. Abeyaratne, The effect of long-range forces on the dynamics of a bar, J. Mech. Phys. Solids., 53 (2005), 705-728.
doi: 10.1016/j.jmps.2004.08.006. |
[13] |
K. Zhou and Q. Du, Mathematical and numerical analysis of linear peridynamic models with nonlocal boundary conditions, SIAM J. Math. Anal., 48 (2010), 1759-1780.
doi: 10.1137/090781267. |
[14] |
K. Zhou and Q. Du, Mathematical analysis for the peridynamic nonlocal continuum theory, Math. Model. Numer. Anal., 45 (2011), 217-234.
doi: 10.1051/m2an/2010040. |
show all references
References:
[1] |
B. Aksoylu and T. Mengesha, Results on nonlocal boundary value problems, Numer. Funct. Anal. Optim., 31 (2010), 1301-1317.
doi: 10.1080/01630563.2010.519136. |
[2] |
A. Buades, B. Coll and J. Morel, Image denoising methods: A new nonlocal principle, SIAM Review, 52 (2010), 113-147.
doi: 10.1137/090773908. |
[3] |
X. Chen and M. Gunzburger, Continuous and discontinuous finite element methods for a peridynamics model of mechanics, Comput. Meth. Appl. Mech. Engrg., 200 (2011), 1237-1250.
doi: 10.1016/j.cma.2010.10.014. |
[4] |
Q. Du, M. Gunzburger, R. Lehoucq and K. Zhou, Analysis and approximation of nonlocal diffusion problems with volume constraints, SIAM Review, 54 (2012), 667-696.
doi: 10.1137/110833294. |
[5] |
Q. Du, L. Tian and X. Zhao, A Convergent Adaptive Finite Element Algorithm for Nonlocal Diffusion and Peridynamic Models, SIAM J. Numer. Anal., 51 (2013), 1211-1234.
doi: 10.1137/120871638. |
[6] |
V. Ervin, N. Heuer and J. Roop, Numerical approximation of a time dependent, non-linear, fractional order diffusion equation, SIAM J. Math. Anal., 45 (2007), 572-591.
doi: 10.1137/050642757. |
[7] |
G. Gilboa and S. Osher, Nonlocal linear image regularization and supervised segmentation, Multiscale Model. Simul., 6 (2007), 595-630.
doi: 10.1137/060669358. |
[8] |
G. Gilboa and S. Osher, Nonlocal operators with applications to image processing, Multiscale Model. Simul., 7 (2008), 1005-1028.
doi: 10.1137/070698592. |
[9] |
M. Gunzburger and R. Lehoucq, A nonlocal vector calculus with application to nonlocal boundary value problems, Multiscale Model. Simul., 8 (2010), 1581-1598.
doi: 10.1137/090766607. |
[10] |
Y. Lou, X. Zhang, S. Osher and A. Bertozzi, Image recovery via nonlocal operators, J. Sci. Comput., 42 (2010), 185-197.
doi: 10.1007/s10915-009-9320-2. |
[11] |
H. Wang and H. Tian, A fast Galerkin method with efficient matrix assembly and storage for a peridynamic model, J. Comput. Phys., 231 (2012), 7730-7738.
doi: 10.1016/j.jcp.2012.06.009. |
[12] |
O. Weckner and R. Abeyaratne, The effect of long-range forces on the dynamics of a bar, J. Mech. Phys. Solids., 53 (2005), 705-728.
doi: 10.1016/j.jmps.2004.08.006. |
[13] |
K. Zhou and Q. Du, Mathematical and numerical analysis of linear peridynamic models with nonlocal boundary conditions, SIAM J. Math. Anal., 48 (2010), 1759-1780.
doi: 10.1137/090781267. |
[14] |
K. Zhou and Q. Du, Mathematical analysis for the peridynamic nonlocal continuum theory, Math. Model. Numer. Anal., 45 (2011), 217-234.
doi: 10.1051/m2an/2010040. |
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