Open Collections

A multiscale method for parabolic equations

Banff International Research Station for Mathematical Innovation and Discovery

We study numerical solutions for parabolic equations with highly varying (multiscale) coefficients. Such equations typically appear when modelling heat diffusion in heterogeneous media like composite materials. For these problems classical polynomial based finite element methods fail to approximate the solution well unless the mesh width resolves the variations in the data. This leads to issues with computational cost and available memory, which calls for new approaches and methods. In this talk I will present a multiscale method based on localized orthogonal decomposition, first introduced by M\r{a}lqvist and Peterseim (2014). The focus will be on how to generalize this method to time dependent problems of parabolic type.

Mathematics; Numerical analysis; Partial differential equations; Women and early careers in math

video/mp4

Author affiliation: KTH Royal Institute of Technology

2019-11-10

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/72242

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/