Invited Lecture
Adapted discretization of partial differential equations generating periodic wavefronts
Università degli Studi dell’Aquila, Italy
Abstract
The talk focuses on the numerical solution of advection-reaction-diffusion problems
by adapted finite difference schemes. The numerical scheme is developed in order
to exploit the a-priori knowledge of the qualitative behaviour of the solution,
gaining advantages in terms of efficiency and accuracy with respect to classical
schemes already known in literature, which mostly rely on algebraic polynomials.
The adaptation is carried out by a non-polynomially fitted space-discretization
and an Implicit-Explicit (IMEX) time-integration. The coefficients of the resulting
numerical scheme depend on unknown parameters to be properly estimated:
such an estimate is performed by an efficient offline minimization of the leading term
of the local truncation error. The effectiveness of this problem-oriented approach is
provided through rigorous theoretical results and selected numerical experiments.
This is a joint work with Beatrice Paternoster, Università degli Studi di Salerno, Italy
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