Numerical approximation of transmission problems across Koch-type highly conductive layers

作者：Lancia Maria Rosaria^*; Cefalo Massimo; Dell'Acqua Guido

来源：Applied Mathematics and Computation, 2012, 218(9): 5453-5473.

DOI：10.1016/j.amc.2011.11.033

• Fractals
• Transmission problems
• Error bounds
• Finite elements

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.

• 出版日期2012-1