University of Birmingham > Talks@bham > Applied Mathematics Seminar Series > Adaptivity and polytopic meshes for convection-diffusion-reaction problems

Adaptivity and polytopic meshes for convection-diffusion-reaction problems

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If you have a question about this talk, please contact Alexandra Tzella.

Real-life models are often characterized by complex geometries and solution features. These make the design of accurate numerical solutions challenging, or even out of reach unless computational resources are smartly allocated.

We advocate the following framework: new FEM approaches allowing for more general partitioning of the computational domain combined with automatic adaptive meshing.

Within this talk, time-space adaptive algorithms based on rigorous a posteriori error bounds will be presented and demonstrated on nonlinear evolution problems with localised features modelling population dynamics and blow-up detection.

We also present two approaches extending the FEM to general meshes while maintaining the ease of implementation and computational cost comparable to that of standard FEM : a discontinuous Galerkin method and the Virtual Element Method (VEM). Both naturally permit the local adaptation of the mesh and the discrete space (eg. polynomial degree), which may be utilised in an automatic fashion.

This talk is part of the Applied Mathematics Seminar Series series.

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