Abstract
The paper applies a conforming P 1 finite element method to general variational inequalities derived from free boundary problems. The domain of the free boundary problem can be properly split into two non-overlapping subdomains where the free boundary is located in only one subdomain. The variational inequality is reduced to a partial differential equation in the subdomain which does not contain the free boundary but still keeps its original form in the other subdomain. Therefore, the original variational inequality can be discretized separately with P 1 finite element in different subdomains. A non-overlapping domain decomposition method is introduced to solve these two discretized sub-problems by P 1 finite element method iteratively while a Robin type boundary condition is utilized for the data transfer on the common boundary. We show that the sequence of such finite element solutions converges to the discretized solution of the original problem. Application to a free seepage problem verifies the theory.
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 callMore From: Computer Methods in Applied Mechanics and Engineering
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.
