ORCID Profile
0000-0003-2514-0408
Current Organisation
Clemson University
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Publisher: Elsevier BV
Date: 10-2021
Publisher: American Mathematical Society (AMS)
Date: 1988
DOI: 10.1090/S0025-5718-1988-0942148-1
Abstract: Recently, Costabel and Stephan in [8] presented convergence proofs for collocation with piecewise linear trial functions for Symm’s integral equation on plane closed curves with corners. In this article we prove the convergence of the above collocation method in the case of open curves. We derive asymptotic error estimates in Sobolev norms and analyze the effect of graded meshes. Numerical experiments based on the implementation of [6] show experimental orders of convergence which confirm our theoretical results on the asymptotic rates of convergence.
Publisher: Elsevier BV
Date: 07-2020
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2007
DOI: 10.1137/060669012
Publisher: Elsevier BV
Date: 1991
Publisher: Elsevier BV
Date: 11-2019
Publisher: Springer Science and Business Media LLC
Date: 11-09-2014
Publisher: American Mathematical Society (AMS)
Date: 26-01-2018
DOI: 10.1090/MCOM/3295
Publisher: Elsevier BV
Date: 06-2023
Publisher: Elsevier BV
Date: 06-2005
Publisher: Elsevier BV
Date: 10-2018
Publisher: Springer Science and Business Media LLC
Date: 1990
DOI: 10.1007/BF00370107
Publisher: Oxford University Press (OUP)
Date: 04-2006
Publisher: Elsevier BV
Date: 04-2015
Publisher: EDP Sciences
Date: 24-10-2019
DOI: 10.1051/M2AN/2019061
Abstract: We develop and analyze a model for the interaction of a quasi-Newtonian free fluid with a poroelastic medium. The flow in the fluid region is described by the nonlinear Stokes equations and in the poroelastic medium by the nonlinear quasi-static Biot model. Equilibrium and kinematic conditions are imposed on the interface. We establish existence and uniqueness of a solution to the weak formulation and its semidiscrete continuous-in-time finite element approximation. We present error analysis, complemented by numerical experiments.
Publisher: Wiley
Date: 10-1990
Publisher: Elsevier BV
Date: 02-2013
Publisher: Wiley
Date: 10-1990
Publisher: Walter de Gruyter GmbH
Date: 19-11-2020
Abstract: In this article, we study the numerical approximation of a variable coefficient fractional diffusion equation. Using a change of variable, the variable coefficient fractional diffusion equation is transformed into a constant coefficient fractional diffusion equation of the same order. The transformed equation retains the desirable stability property of being an elliptic equation. A spectral approximation scheme is proposed and analyzed for the transformed equation, with error estimates for the approximated solution derived. An approximation to the unknown of the variable coefficient fractional diffusion equation is then obtained by post-processing the computed approximation to the transformed equation. Error estimates are also presented for the approximation to the unknown of the variable coefficient equation with both smooth and non-smooth diffusivity coefficient and right-hand side. Numerical experiments are presented to test the performance of the proposed method.
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2013
DOI: 10.1137/120861631
Publisher: Hindawi Limited
Date: 2001
DOI: 10.1155/S1024123X01001521
Abstract: We investigate fluid transport in random velocity fields with unsteady drift. First, we propose to quantify fluid transport between flow regimes of different characteristic motion, by escape probability and mean residence time. We then develop numerical algorithms to solve for escape probability and mean residence time, which are described by backward Fokker-Planck type partial differential equations. A few computational issues are also discussed. Finally, we apply these ideas and numerical algorithms to a tidal flow model.
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2009
DOI: 10.1137/070708354
Publisher: Elsevier
Date: 1984
Publisher: Elsevier BV
Date: 09-1999
Publisher: Elsevier BV
Date: 06-2008
Publisher: Wiley
Date: 05-1996
DOI: 10.1002/(SICI)1098-2426(199605)12:3<333::AID-NUM4>3.0.CO;2-P
Publisher: Springer Science and Business Media LLC
Date: 16-01-2021
Publisher: Elsevier BV
Date: 11-2011
Publisher: Elsevier BV
Date: 04-2000
Publisher: Springer Science and Business Media LLC
Date: 1999
Publisher: Wiley
Date: 1999
DOI: 10.1002/(SICI)1098-2426(199901)15:1<91::AID-NUM5>3.0.CO;2-T
Publisher: Wiley
Date: 31-05-2006
DOI: 10.1002/NUM.20090
Publisher: Elsevier BV
Date: 03-2021
Publisher: MDPI AG
Date: 06-11-2015
Publisher: Elsevier BV
Date: 1992
Publisher: Springer Science and Business Media LLC
Date: 28-01-2017
Publisher: Wiley
Date: 29-10-2003
DOI: 10.1002/NUM.10086
Publisher: Elsevier BV
Date: 08-2013
Publisher: Elsevier BV
Date: 2006
Publisher: Elsevier BV
Date: 02-2021
Publisher: Wiley
Date: 18-12-2003
DOI: 10.1002/MMA.432
Publisher: Elsevier BV
Date: 12-1993
Publisher: Elsevier BV
Date: 04-2001
Publisher: Informa UK Limited
Date: 1994
Publisher: Wiley
Date: 02-09-2018
DOI: 10.1002/NUM.22303
Publisher: Wiley
Date: 2007
DOI: 10.1002/NUM.20169
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2007
DOI: 10.1137/050642757
Publisher: Elsevier BV
Date: 04-2006
Publisher: Elsevier BV
Date: 2023
DOI: 10.2139/SSRN.4467083
Publisher: Elsevier BV
Date: 2017
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2012
DOI: 10.1137/100782048
Publisher: Elsevier BV
Date: 06-1996
Publisher: Elsevier BV
Date: 05-2011
Publisher: Springer Science and Business Media LLC
Date: 16-09-2020
Publisher: Wiley
Date: 06-1991
Publisher: Elsevier BV
Date: 03-2000
Publisher: AIP Publishing
Date: 04-2000
DOI: 10.1063/1.533228
Abstract: In this paper the difference in the asymptotic dynamics between the nonlocal and local two-dimensional Swift–Hohenberg models is investigated. It is shown that the bounds for the dimensions of the global attractors for the nonlocal and local Swift–Hohenberg models differ by an absolute constant, which depends only on the Rayleigh number, and upper and lower bounds of the kernel of the nonlocal nonlinearity. Even when this kernel of the nonlocal operator is a constant function, the dimension bounds of the global attractors still differ by an absolute constant depending on the Rayleigh number.
Publisher: Wiley
Date: 30-07-2005
DOI: 10.1002/NUM.20038
Publisher: Elsevier BV
Date: 05-2013
Publisher: Elsevier BV
Date: 10-2009
Publisher: Elsevier BV
Date: 2016
Publisher: Elsevier BV
Date: 10-2012
Publisher: Elsevier BV
Date: 09-2007
Publisher: Wiley
Date: 2006
DOI: 10.1002/NUM.20112
Publisher: Elsevier BV
Date: 03-2008
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2011
DOI: 10.1137/100794250
Publisher: Elsevier BV
Date: 05-2005
Publisher: Elsevier BV
Date: 11-1992
Publisher: Elsevier BV
Date: 03-1998
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2000
Publisher: Elsevier BV
Date: 03-1999
Publisher: Elsevier BV
Date: 05-2005
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2003
Publisher: Springer Science and Business Media LLC
Date: 1988
DOI: 10.1007/BF00317059
Location: United Kingdom of Great Britain and Northern Ireland
Start Date: 2004
End Date: 2008
Funder: Directorate for Mathematical & Physical Sciences
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