3,595 research outputs found
Layer-adapted meshes for singularly perturbed problems via mesh partial differential equations and a posteriori information
We propose a new method for the construction of layer-adapted meshes for
singularly perturbed differential equations (SPDEs), based on mesh partial
differential equations (MPDEs) that incorporate \emph{a posteriori} solution
information. There are numerous studies on the development of parameter robust
numerical methods for SPDEs that depend on the layer-adapted mesh of Bakhvalov.
In~\citep{HiMa2021}, a novel MPDE-based approach for constructing a
generalisation of these meshes was proposed. Like with most layer-adapted mesh
methods, the algorithms in that article depended on detailed derivations of
\emph{a priori} bounds on the SPDE's solution and its derivatives. In this work
we extend that approach so that it instead uses \emph{a posteriori} computed
estimates of the solution. We present detailed algorithms for the efficient
implementation of the method, and numerical results for the robust solution of
two-parameter reaction-convection-diffusion problems, in one and two
dimensions. We also provide full FEniCS code for a one-dimensional example.Comment: 15 pages, 5 figures, FEniCS cod
Three-dimensional finite element modelling of stack pollutant emissions
In this paper we propose a finite element method approach formodelling the air quality in a local scale over complex terrain. The area of interest is up to tens of kilometres and it includes pollutant sources. The proposed methodology involves the generation of an adaptive tetrahedral mesh, the computation of an ambient wind field, the inclusion of the plume rise effect in the wind field, and the simulation of transport and reaction of pollutants. The methodology is used to simulate a fictitious pollution episode in La Palma island (Canary Island, Spain).Peer ReviewedPostprint (published version
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