Convergence of the FEM in domains with external cusps.

GABRIEL ACOSTA, GABRIELA ARMENTANO

Santiago de Chile

Congreso; Santiago Numérico II; 2010

Facultad de Matemáticas, Pontificia Universidad Católica de Chile

In [1] the finite element method was applied to a nonhomogeneous Neumann problem on a cuspidal domain $Omega$ of R2, and using regularity results developed in [2], quasioptimal order error estimates in the energy norm were obtained for certain graded meshes. In this talk we present similar results for the error in the L2 norm. Since many classical results in the theory of Sobolev spaces do not apply to the domain under consideration, our estimates require a particular duality treatment working on appropriate weighted spaces. Our talk is based on the recent article [3]. References [1] G. Acosta, M. G. Armentano, R. G. Duran and A. L. Lombardi, Finite element approximations in a nonLipschitz domain, SIAM Journal on Numerical Analysis 45(1), 277-295 (2007). [2] G. Acosta, M. G. Armentano, R. G. Durn and A. L. Lombardi, Nonhomogeneous Neumann problem for the Poisson equation in domains with an external cusp, Journal of Mathematical Analysis and Applications 310(2), 397-411 (2005). [3] G. Acosta, M. G. Armentano, Finite element approximations in a nonLipschitz domain: Part II, To Appear in Math. Comp.