Abstract
In this paper, an Interior Penalty Discontinuous Galerkin (IPDG) finite element method is analyzed for approximating quasilinear parabolic equations. The equations can be characterized as perturbed parabolic p-Laplacian equations. The fully discrete scheme is obtained by applying s-stage Diagonally Implicit Runge–Kutta (s-DIRK) methods for the time integration. The nonlinear systems of the algebraic equations appearing in s-DIRK cycles are solved by developing two low storage Picard iterative processes. A stability bound is shown for the semi-discrete IPDG solution in the broken ‖.‖DG,p-norm. Continuous in time a priori error estimates are proved in case of p>2, when linear approximation space is used. A numerical test is performed in order to compare the performance of the two Picard iterative processes. Also, the results presented in the theoretical analysis are confirmed by numerical examples.
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.
