Abstract
AbstractWe introduce function spaces useful for the analysis of elliptic equations and for the error estimate of the finite element method. In particular, we review Sobolev spaces and the important properties of functions in these spaces, including the extension, embedding, and trace theorems. We also discuss the well-posedness and regularity estimates for elliptic boundary value problems in Sobolev spaces. In turn, we present key steps to derive the finite element error analysis. The trace and regularity results usually depend on the smoothness of the domain, and the nonsmooth points on the boundary can lead to singularities in the solution. For the conciseness of the presentation, some results are summarized without proofs. Readers will be referred to specific references for more details. This chapter is suitable for readers who need a review of basic results in Sobolev spaces and who are starting to work on finite element error analysis for elliptic equations.
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.
