\(H^3\) and \(H^4\) Regularities of the Poisson Equation on Polygonal Domains
This paper presents two equalities of \(H^3\) and \(H^4\) semi-norms for the solutions of the Poisson equation in a two-dimensional polygonal domain. These equalities enable us to obtain higher order constructive a priori error estimates for finite element approximation of the Poisson equation with validated computing.
KeywordsPoisson equation A priori estimates
This work was supported by the Grant-in-Aid from the Ministry of Education, Culture, Sports, Science and Technology of Japan (Nos. 15H03637, 15K05012) and supported by Program for Leading Graduate Schools “Training Program of Leaders for Integrated Medical System for Fruitful Healthy-Longevity Society.”