A Crank-Nicolson scheme for the Dirichlet-to-Neumann semigroup (Q2336933)
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| Language | Label | Description | Also known as |
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| English | A Crank-Nicolson scheme for the Dirichlet-to-Neumann semigroup |
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A Crank-Nicolson scheme for the Dirichlet-to-Neumann semigroup (English)
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19 November 2019
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Summary: 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.
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