A Crank-Nicolson Scheme for the Dirichlet-to-Neumann Semigroup
Copyright policy )A Crank-Nicolson Scheme for the Dirichlet-to-Neumann Semigroup
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 aP1finite element scheme for the problem, and we illustrate this convergence by means of a FreeFem++ implementation.
Finite difference methods for boundary value problems involving PDEs, Dirichlet-to-Neumann semigroup, QA1-939, Crank-Nicolson, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], General theory of numerical analysis in abstract spaces, Mathematics
Finite difference methods for boundary value problems involving PDEs, Dirichlet-to-Neumann semigroup, QA1-939, Crank-Nicolson, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], General theory of numerical analysis in abstract spaces, Mathematics
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