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

الملخص EN

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 P 1 finite element scheme for the problem, and we illustrate this convergence by means of a FreeFem++ implementation.