Error Estimation for Advection-Diffusion Equation
The space-time Advective-Diffusive (AD) systems arise in computational fluid
dynamics, gas dynamics, semiconductor devices etc. The space-time
Galerkin least squares (GLS) finite element method has been successful
as a numerical method in the solution of these time-dependent
equations. These problems typically have very steep gradients and
sharp discontinuities. In order to obtain accurate solutions at a
reasonable computational expense, one has to resort to adaptive finite
element methods. We have developed a novel a posteriori error estimate
for the GLS formulation of a prototypical scalar steady AD equation.
A variety of error estimation techniques have been proposed for linear
elliptic symmetric positive-definite problems. Their extension to
other equations is an active research area. One asymptotically exact
residual-based error indicator for elliptic Poisson problems relies on
solving local Neumann problems in each element. We extend this
approach to the unsymmetric and positive semi-definite AD operator.
Existing error estimates for the steady AD equation, discard the
advection term in order to stabilize the local error problem. In our
formulation, we retain the advection terms and impart stability by
including a least squares term. We call this new method the
Stabilized Element Residual Method .
Amit Agarwal (agarwal@gloworm.Stanford.EDU)
AEL 211 (Ph: 415-725-0458)
Integrated Circuits Laboratory
Stanford University
Stanford, CA 94305-4055