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A time‐space FCT‐FE formulation for 1D time dependent advection‐diffusion equation
Author(s) -
Feng Dianlei,
Neuweiler Insa,
Nackenhorst Udo
Publication year - 2018
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201800244
Subject(s) - discretization , space time , advection , monotonic function , discontinuous galerkin method , convection–diffusion equation , diffusion , mathematics , finite element method , interpolation (computer graphics) , courant–friedrichs–lewy condition , spacetime , diffusion equation , temporal discretization , weak formulation , mathematical analysis , computer science , physics , boundary value problem , engineering , metric (unit) , operations management , thermodynamics , animation , computer graphics (images) , quantum mechanics , chemical engineering
We present a time‐space flux‐corrected transport (FCT) finite element formulation for solving the linear time‐dependent advection dominated advection‐diffusion equation. Solving advection dominated transport equations with conventional finite element (FE) methods suffers from drawbacks of excessive numerical dispersion which results in non‐physical, non‐monotonic solutions. The FCT algorithm is an effective method which suppresses the non‐monotonic behavior of the solution by applying a limited anti‐diffusion operator to a first order scheme. Applying the FCT algorithm to time‐space FE formulation, such as the time‐discontinuous Galerkin (TDG) method, benefits from the advantages of both the TDG scheme and the FCT algorithm. In another word, the time‐space FCT‐FE formulation achieves arbitrary odd order accuracy in time at the discontinuous time nodes. Large time steps can be applied and the scheme ensures monotonic solution when linear interpolation is used for spatial discretization.