INTERNODES is a general method to deal with non-conforming discretizations of second order partial differential equations on regions partitioned into two or several subdomains. It exploits two intergrid interpolation operators, one for transferring the Dirichlet trace across the interface, the others for the Neumann trace. In every subdomain the original problem is discretized by the finite element method, using a priori non-matching grids and piece-wise polynomials of different degree. In this paper we provide several interpretations of the method and we carry out its stability and convergence analysis, showing that INTERNODES exhibits optimal convergence rate with respect to the finite element sizes. Finally we propose an efficient algorithm for the solution of the corresponding algebraic system.

Analysis of the INTERNODES method for non-conforming discretizations of elliptic equations

Gervasio, Paola
;
QUARTERONI, Alfio
2018-01-01

Abstract

INTERNODES is a general method to deal with non-conforming discretizations of second order partial differential equations on regions partitioned into two or several subdomains. It exploits two intergrid interpolation operators, one for transferring the Dirichlet trace across the interface, the others for the Neumann trace. In every subdomain the original problem is discretized by the finite element method, using a priori non-matching grids and piece-wise polynomials of different degree. In this paper we provide several interpretations of the method and we carry out its stability and convergence analysis, showing that INTERNODES exhibits optimal convergence rate with respect to the finite element sizes. Finally we propose an efficient algorithm for the solution of the corresponding algebraic system.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

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/11379/502493
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 12
  • ???jsp.display-item.citation.isi??? 9
social impact