In this paper, we propose the mathematical and finite element analysis of a second-order partial differential equation endowed with a generalized Robin boundary condition which involves the Laplace--Beltrami operator by introducing a function space $H^1(Omega; Gamma)$ of $H^1(Omega)$-functions with $H^1(Gamma)$-traces, where $Gamma subseteq partial Omega$. Based on a variational method, we prove that the solution of the generalized Robin boundary value problem possesses a better regularity property on the boundary than in the case of the standard Robin problem. We numerically solve generalized Robin problems by means of the finite element method with the aim of validating the theoretical rates of convergence of the error in the norms associated to the space $H^1(Omega; Gamma)$.

Well-posedness, regularity, and convergence analysis of the finite element approximation of a generalized Robin boundary value problem

COLCIAGO, CLAUDIA MARIA;DEDE', LUCA;QUARTERONI, ALFIO MARIA
2015-01-01

Abstract

In this paper, we propose the mathematical and finite element analysis of a second-order partial differential equation endowed with a generalized Robin boundary condition which involves the Laplace--Beltrami operator by introducing a function space $H^1(Omega; Gamma)$ of $H^1(Omega)$-functions with $H^1(Gamma)$-traces, where $Gamma subseteq partial Omega$. Based on a variational method, we prove that the solution of the generalized Robin boundary value problem possesses a better regularity property on the boundary than in the case of the standard Robin problem. We numerically solve generalized Robin problems by means of the finite element method with the aim of validating the theoretical rates of convergence of the error in the norms associated to the space $H^1(Omega; Gamma)$.
2015
A priori error estimation; Finite element method; Generalized Robin boundary conditions; Isoparametric analysis; Laplace-Beltrami operator; Poisson equation; Regularity of solution; Well-posedness; Numerical Analysis
File in questo prodotto:
File Dimensione Formato  
11311-990589 Quarteroni.pdf

accesso aperto

: Post-Print (DRAFT o Author’s Accepted Manuscript-AAM)
Dimensione 506.91 kB
Formato Adobe PDF
506.91 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/990589
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 27
  • ???jsp.display-item.citation.isi??? 22
social impact