Mixed function space on two meshes

1

Hi all,

I was wondering if FEniCS can do the following:
mesh1 = UnitCubeMesh(5,5,5)
mesh2 = UnitCubeMesh(7,7,7) % or the second mesh is a submesh of mesh1
V1 = FunctionSpace(mesh1,‘CG’,1)
V2 = FunctionSpace(mesh2,‘CG’,1)
then how to construct the mixed function space of V1*V2 and define the variational form based on this mixed function space? Thanks in advance.

JY

2

What are you trying to achieve with a product of function spaces on two differently sized meshes?
Have you considered https://arxiv.org/pdf/1911.01166.pdf and the corresponding code: GitHub - cdaversin/mixed-dimensional-examples: Code to reproduce numerical examples presented in "Abstractions and automated algorithms for mixed-dimensional finite element methods" (2019) ?

1 Like
3

Thanks for the reply, dokken. However, when i use FEniCS (version 2019.1.0) to run the code, it implies that ‘MixedFunctionSpace’ is not defined. Do I need to install some other library or this is defined in develop verision? Thanks again.

4

You Need to use the development version of fenics, which can be accessed through for instance docker: quay.io/fenicsproject/dev:latest

It should also be available through apt-get install on ubuntu 20.04 as far as Im aware.

5

Thanks for this. really appreciate that!