A Crank‐Nicolson Scheme for the Dirichlet‐to‐Neumann Semigroup

Rola Ali Ahmad, Toufic El Arwadi, Houssam Chrayteh and Jean-Marc Sac-Epée

Journal of Applied Mathematics, 2015, vol. 2015, issue 1

Abstract: The aim of this work is to study a semidiscrete Crank‐Nicolson type scheme in order to approximate numerically the Dirichlet‐to‐Neumann semigroup. We construct an approximating family of operators for the Dirichlet‐to‐Neumann semigroup, which satisfies the assumptions of Chernoff’s product formula, and consequently the Crank‐Nicolson scheme converges to the exact solution. Finally, we write a P1 finite element scheme for the problem, and we illustrate this convergence by means of a FreeFem++ implementation.

Date: 2015
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https://doi.org/10.1155/2015/429641

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2015:y:2015:i:1:n:429641

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