Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
FINITE ELEMENT APPROXIMATIONS IN A NON-LIPSCHITZ DOMAIN: GABRIEL ACOSTA AND MARIA G. ARMENTANO
 

Summary: FINITE ELEMENT APPROXIMATIONS IN A NON-LIPSCHITZ DOMAIN:
PART II
GABRIEL ACOSTA AND MAR´IA G. ARMENTANO
Abstract. In [2] the finite element method was applied to a non-homogeneous Neumann prob-
lem on a cuspidal domain R2
, and quasi-optimal order error estimates in the energy norm
were obtained for certain graded meshes. In this paper, we study the error in the L2
norm
obtaining similar results by using graded meshes of the type considered in [2]. Since many
classical results in the theory Sobolev spaces do not apply to the domain under consideration,
our estimates require a particular duality treatment working on appropriate weighted spaces.
On the other hand, since the discrete domain h verifies h, in [2] the source term of
the Poisson problem was taken equal to 0 outside in the variational discrete formulation. In
this article we also consider the case in which this condition does not hold and obtain more
general estimates, which can be useful in different problems, for instance in the study of the
effect of numerical integration, or in eigenvalue approximations.
1. introduction
The finite element method has been widely studied in several contexts involving different kinds
of differential equations, however, the domains under consideration are in general polygons or
smooth domains. In the recent paper [2], the piecewise linear finite element method was applied

  

Source: Armentano, María Gabriela - Departamento de Matemática, Universidad de Buenos Aires

 

Collections: Mathematics