Numerical methods for spectral problems: theory and applications
Verified pointwise evaluation for Poisson's equation via hypercircle method
*Xuefeng LIU (Niigata University)
The hypercircle method is a useful tool to investigate the error of approximation solution to boundary value problems. Such a method is proposed by W. Prager and J. Synge in 1947 and by H. Fujita in 1955. Particularly, the version of Fujita has the potential to provide rigorous estimation for the pointwise value of exact solution. In this talk, we will take a survey of the research on hypercircle method and introduce the result of pointwise evaluation by combining Fujita's method and the finite element method.