Improved interpolation nodes for RT and N1curl elements. #52

wence- · 2020-06-10T16:08:29Z

This is mostly work by @FabianL1908

Addresses #40.

wence-

Some drive-by comments.

FIAT/brezzi_douglas_marini.py

FIAT/functional.py

FIAT/nedelec.py

FIAT/nedelec_second_kind.py

rckirby · 2020-06-15T13:51:19Z

Is there a "pure FIAT"-level test we could devise that would test these new nodes are a thing?

FIAT/brezzi_douglas_marini.py

FIAT/check_format_variant.py

FIAT/functional.py

FIAT/nedelec.py

wence- · 2020-06-26T18:09:21Z

@FabianL1908 I think the only outstanding question here is if we can test these elements in FIAT. We could add these variants to the test/unit/test_fiat.py file (since they continue to be nodal).

FabianL1908 · 2020-06-26T22:34:01Z

@wence- I added the tests for the new variants. They were actually helpful since helped me to spot a small bug. Do you think that are enough tests or do you have more in mind?

wence- · 2020-06-29T17:11:48Z

Do you think that are enough tests or do you have more in mind?

Maybe check that the error-checking for specifying quadrature for the integral representation by hand that is too low works. Since the code is repeated, you only need to do it for one element I think.

You can do this by doing:

import pytest


def test_....():
   with pytest.raises(WhateverTheExceptionWas):
       MakeElement(cell, ..., variant="integral(degree-that-is-too-low)")

FabianL1908 · 2020-06-29T18:02:09Z

I have added the test for two elements, since the bound is slightly different for N1curl and N2curl.

FIAT/brezzi_douglas_marini.py

FIAT/nedelec.py

FIAT/raviart_thomas.py

test/unit/test_fiat.py

wence- · 2020-07-14T11:09:45Z

I rebased and squashed things, and addressed the final comments. I think this is good to go.

Although the existing FIAT functionals are fine for tabulation and hence normal finite element assembly, they under-integrate for the purposes of interpolation. This results in sub-optimal convergence in the H(div/curl) norm of the interpolation error, which should be (for example) ||u - I_q u||_H(div, T) \le C h^q |u|_H^{q+1}(T) for RTq elements. To fix this, implement the dual basis using "textbook" integral moment functionals (even on edges). These functionals are selected by creating the element with an appropriate variant string on construction.

wence- force-pushed the wence/feature/interpolation-nodes branch from d4b679a to 5278b42 Compare June 10, 2020 16:22

wence- commented Jun 10, 2020

View reviewed changes

This was referenced Jun 10, 2020

Variants for BDM/RT and Nedelec spaces. FInAT/FInAT#56

Merged

Handle variants for RT and Nedelec spaces firedrakeproject/tsfc#217

Merged

Better nodes for RT/Nedelec #40

Closed