A posteriori error estimates for nonconforming approximations of Steklov eigenvalue problems

• Autores: Dello Russo, Anahí; Alonso, Ana Esther
• Año de publicación: 2011
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: Matemática; A posteriori error estimates; Nonconforming finite element methods; Steklov eigenvalue problem
• Institución: Universidad Nacional de La Plata

This paper deals with a posteriori error estimators for the non conforming CrouzeixRaviart finite element approximations of the Steklov eigenvalue problem. First, we define an error estimator of the residual type which can be computed locally from the approximate eigenpair and we prove the equivalence between this estimator and the broken energy norm of the error with constants independent of the corresponding eigenvalue. Next, we prove that edge residuals dominate the volumetric part of the residual and that the volumetric part of the residual terms dominate the normal component of the jumps of the discrete fluxes across interior edges. Finally, based on these results, we introduce two simpler equivalent error estimators. The analysis shows that these a posteriori error estimates are optimal up to higher order terms and that may be used for the design of adaptive algorithms.
Facultad de Ciencias Exactas