Finite element algorithms for transport-diffusion problems: stability, adaptivity, tractability

• Autores: Endre Süli
• Localización: Proceedings oh the International Congress of Mathematicians: Madrid, August 22-30,2006 : invited lectures / coord. por Marta Sanz Solé , Javier Soria de Diego , Juan Luis Varona Malumbres , Joan Verdera , Vol. 3, 2006, ISBN 978-3-03719-022-7, págs. 1271-1298
• Idioma: inglés
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• Resumen

  • Partial differential equations with nonnegative characteristic form arise in numerous mathematical models of physical phenomena: stochastic analysis, in particular, is a fertile source of equations of this kind. We survey recent developments concerning the finite element approximation of these equations, focusing on three relevant aspects: (a) stability and stabilisation;

    (b) hp-adaptive algorithms driven by residual-based a posteriori error bounds, capable of automatic variation of the granularity h of the finite element partition and of the local polynomial degree p; (c) complexity-reduction for high-dimensional transport-diffusion problems by stabilised sparse finite element methods.