Abstract
In this paper, we introduce a new method to analyze the convergence of the standard finite element method for a class of elliptic quasi-variational inequalities (QVIs) with non-linear source terms. It consists of approximating the solution of the non-linear QVI by a sequence of solutions of linear QVIs. Under a realistic assumption on the non-linearity, we first prove that the resulting iterative scheme is geometrically convergent to the solution of the QVI. Afterwards, we establish an error estimate in the maximum norm between the continuous iterative scheme and its finite element counterpart. Finally, combining this latter estimate with the geometrical convergence of the iterative scheme, we also derive an error estimate between the solution of the QVI and its finite element counterpart.
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 callMore From: Indian Journal of Industrial and Applied Mathematics
Disclaimer: 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.
