A Taylor–Galerkin method for convective transport problems

摘要: A method is described to derive finite element schemes for the scalar convection equation in one or more space dimensions. To produce accurate temporal differencing, employs forward-time Taylor series expansions including time derivatives of second- and third-order which are evaluated from governing partial differential equation. This yields a generalized time-discretized successively discretized by means standard Bubnov–Galerkin method. The technique illustrated first dimension. With linear elements Euler, leap-frog Crank–Nicolson stepping, several interesting relations with Galerkin recently developed Petrov–Galerkin methods emerge new Taylor–Galerkin found exhibit particularly high phase-accuracy minimal numerical damping. extended deal variable coefficient problems multi-dimensional situations.