Key, K., Baidoo, F. A., Elgeti, S., & Hughes, T. J. R. (2023, June 19). Residual-Based Variational Stabilization of Isogeometric Finite Element Methods for Advection-Diffusion-Reaction Problems [Conference Presentation]. 11th International Conference on IsoGeometric Analysis (IGA 2023), Lyon, France. http://hdl.handle.net/20.500.12708/187755
Some engineering applications can be represented by Advection-Diffusion-Reaction (ADR) problems. Such ADR problems are oftentimes numerically analyzed; for example, by using Galerkin Finite Element Methods (FEMs). In fact, Galerkin FEMs are very popular and their results are proven to converge. Still, real-world Galerkin results frequently suffer from spurious oscillations as sharp layers (which are often present, e.g., at boundaries) are not adequately resolved. Sufficiently resolving such sharp layers is usually — and especially for multidimensional problems — infeasible due to the resulting huge computational costs. This drastic proliferation of computational costs can be mitigated by modifying the variational formulations instead of their discretizations (see, e.g., [1]).
We will concern ourselves with a conservative and concise residual-based variational stabilization of isogeometric FEMs for ADR problems. In particular, the proposed stabilization recovers the results from [2] and [3] for the AD and RD limits, respectively. Furthermore, the one-dimensional stabilization is extended to multidimensional settings in an untraditional manner: the variational methods instead of their stabilization parameters are generalized.
[1] G. Hauke, G. Sangalli, and M.H. Doweidar. Combining Adjoint Stabilized Methods for the Advection-Diffusion-Reaction Problem. Mathematical Models and Methods in Applied Sciences, Vol. 17, 2:305–326, 2007.
[2] A.N. Brooks, and T.J.R. Hughes. Streamline Upwind/Petrov-Galerkin Formulations for Convection Dominated Flows with Particular Emphasis on the Incompressible Navier-Stokes Equations. Computer Methods in Applied Mechanics and Engineering, 32:199–259, 1982.
[3] L.P. Franca, and E.G. Dutra Do Carmo. The Galerkin Gradient Least-Squares Method. Computer Methods in Applied Mechanics and Engineering, 74:41–54, 1989.
en
Project (external):
Deutsche Forschungsgemeinschaft (DFG)
-
Project ID:
333849990/GRK2379
-
Research Areas:
Mathematical and Algorithmic Foundations: 40% Modeling and Simulation: 40% Fundamental Mathematics Research: 20%