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Residual-Based Error Estimation for Finite Difference and Finite Volume Schemes

Tuesday, February 8, 3:30PM
ACES 6.304

Christopher J. Roy

In computational mechanics, the discretization error is often the largest and most difficult numerical approximation error to estimate. While the finite element community has a rich history in residual-based error estimation, these techniques are not easily extended to other discretization schemes. This talk will present a new framework for developing residual-based error estimation methods for finite difference and finite volume schemes, the two approaches most commonly used for computational fluid dynamics. This framework is based on the Generalized Truncation Error Expression which relates the discrete equations to the governing partial differential or integral equations in a very general manner. The residual-based error estimation methods to be discussed include error transport equations, defect correction, and adjoint methods, all three of which can be developed in either continuous or discrete form. Approaches for assessing the reliability of these error estimators will also be discussed. Finally, the role of residuals in solution adaptation will be briefly mentioned.

Host: S. Prudhomme