Convergence of Lowest Order Semi-Lagrangian Schemes

• Published in: Foundations of computational mathematics Vol. 13; no. 2; pp. 187 - 220
• Main Authors: Heumann, Holger, Hiptmair, Ralf
• Format: Journal Article
• Language: English
• Published: New York Springer-Verlag 01.04.2013; Springer; Springer Nature B.V; Springer Verlag
• Subjects: Applications of Mathematics; Approximation; Asymptotic properties; Boundary conditions; Computational mathematics; Computer Science; Convergence; Convergence (Mathematics); Differential equations; Discretization; Economics; Estimates; Foundations; Galerkin methods; Lagrangian functions; Linear and Multilinear Algebras; Math Applications in Computer Science; Mathematical analysis; Mathematical models; Mathematics; Mathematics and Statistics; Matrix Theory; Numerical Analysis; Switzerland; Advection-diffusion problem; 65m60; 65m25; Semi-Lagrangian methods; 65m12; Discrete differential forms

We consider generalized linear transient advection-diffusion problems for differential forms on a bounded domain in ℝ d . We provide comprehensive a priori convergence estimates for their spatiotemporal discretization by means of a first-order in time semi-Lagrangian approach combined with a discont...