Abstract
Based on Landau-type transformation, a unidimensional single phase Stefan problem is transformed into a system consisting of parabolic equation with a quadratic nonlinear term and two ordinary differential equations. An Hl-Galerkin method is then applied to estimate the quadratic nonlinear term effectively and optimal estimates in L∞, L2, H1 and H2 norms are obtained without quasiuniformity condition on the finite element mesh. Further using quasiprojection technique, negative norm estimates and superconvergence results are derived. As a result, Galerkin approximation for the free boundary exhibits a superconvergence phenomenon. Since the superconvergence results for the Hl– Galerkin approximations to nonlinear parabolic equations are not available in the literature, the present study has an added significance.
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.
