Abstract
We consider discrete schemes for a nonlinear model of non-Fickian diffusion in viscoelastic polymers. The model is motivated by, but not the same as, that proposed by Cohen, White, and Witelski in SIAM J. Appl. Math., 55 (1995), pp. 348-368. The spatial discretization is effected with both the symmetric and nonsymmetric interior penalty discontinuous Galerkin finite element method, and the time discretization is of Crank-Nicolson type. We also discuss two means of handling the nonlinearity: either implicitly, which requires the solution of nonlinear equations at each time level, or through a linearization based on extrapolating from previous time levels. The same optimal orders of convergence are proven in both cases and, to verify this, some numerical results are also given for the linearized scheme.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
