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Regularity properties of solutions of elliptic equations in R 2 in limit cases

Angela Alberico, Vincenzo Ferone (1995)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In this paper the Dirichlet problem for a linear elliptic equation in an open, bounded subset of R 2 is studied. Regularity properties of the solutions are proved, when the data are L 1 -functions or Radon measures. In particular sharp assumptions which guarantee the continuity of solutions are given.

Remarques sur les équations linéaires elliptiques du second ordre sous forme divergence dans les domaines non bornés

Pierre Louis Lions (1985)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si dimostra resistenza e l'unicità della soluzione del problema A u = f , u H 0 1 ( Ω ) nel caso in cui Ω è un aperto di n non limitato, A è un operatore variazionale ellittico del secondo ordine a coefficienti misurabili e limitati e f appartiene a H - 1 ( Ω ) .

Residual and hierarchical a posteriori error estimates for nonconforming mixed finite element methods

Linda El Alaoui, Alexandre Ern (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We analyze residual and hierarchical a posteriori error estimates for nonconforming finite element approximations of elliptic problems with variable coefficients. We consider a finite volume box scheme equivalent to a nonconforming mixed finite element method in a Petrov–Galerkin setting. We prove that all the estimators yield global upper and local lower bounds for the discretization error. Finally, we present results illustrating the efficiency of the estimators, for instance, in the simulation...

Residual and hierarchical a posteriori error estimates for nonconforming mixed finite element methods

Linda El Alaoui, Alexandre Ern (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We analyze residual and hierarchical a posteriori error estimates for nonconforming finite element approximations of elliptic problems with variable coefficients. We consider a finite volume box scheme equivalent to a nonconforming mixed finite element method in a Petrov–Galerkin setting. We prove that all the estimators yield global upper and local lower bounds for the discretization error. Finally, we present results illustrating the efficiency of the estimators, for instance, in the simulation...

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