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Monday, April 27, 2015
10:00 AM - 11:00 AM
CNLS Conference Room (TA-3, Bldg 1690)


Limiting techniques for discontinuous and continuous finite elements

Prof. D. Kuzmin
Institute of Applied Mathematics, Dortmund University of Technology

In this talk, we present and compare some multidimensional limiting techniques for enforcing geometric and algebraic maximum principles in finite element methods for convection-dominated transport equations. In the context of discontinuous Galerkin (DG) methods, undershoots and overshoots are eliminated by limiting the derivatives of the Taylor polynomial representing a finite element shape function. The antidiffusive part of a continuous (linear or bilinear) Galerkin approximation is constrained using flux-corrected transport (FCT) algorithms formulated in terms of edge or element contributions. We show that the element-based approach offers more flexibility in the choice of algorithmic ingredients (low-order scheme, high-order scheme, time stepping, limiting strategy) than its edge-based counterpart. In particular, we introduce a localized FCT limiter which has the same structure as the Barth-Jespersen limiter for DG and finite volume methods. An anisotropic version of this limiter may be used to constrain directional derivatives in situations when the use of a common correction factor for all components gives rise to strong smearing or nonphysical ripples.

Host: Misha Shashkov