Efficient high-order time discretization methods for PDEs

May 8-10, 2019 - Villa Orlandi, Anacapri, Italy

Invited Lecture

Adapted discretization of partial differential equations generating periodic wavefronts

Raffaele D’Ambrosio,

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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