We prove a priori error estimates for a parabolic second order transmission problem across a prefractal interface K-n of Koch type which divides a given domain Omega into two non-convex sub-domains Omega(i)(n). By exploiting some regularity results for the solution in Omega(i)(n) we build a suitable mesh, compliant with the so-called "Grisvard" conditions, which allows to achieve an optimal rate of convergence for the semidiscrete approximation of the prefractal problem by Galerkin method. The discretization in time is carried out by the theta-method. (C) 2011 Elsevier Inc. All rights reserved.
Numerical approximation of transmission problems across Koch-type highly conductive layers / Lancia, Maria Rosaria; Cefalo, Massimo; Guido, Dell'Acqua. - In: APPLIED MATHEMATICS AND COMPUTATION. - ISSN 0096-3003. - 218:9(2012), pp. 5453-5473. [10.1016/j.amc.2011.11.033]
Numerical approximation of transmission problems across Koch-type highly conductive layers
LANCIA, Maria Rosaria;CEFALO, Massimo;
2012
Abstract
We prove a priori error estimates for a parabolic second order transmission problem across a prefractal interface K-n of Koch type which divides a given domain Omega into two non-convex sub-domains Omega(i)(n). By exploiting some regularity results for the solution in Omega(i)(n) we build a suitable mesh, compliant with the so-called "Grisvard" conditions, which allows to achieve an optimal rate of convergence for the semidiscrete approximation of the prefractal problem by Galerkin method. The discretization in time is carried out by the theta-method. (C) 2011 Elsevier Inc. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
