Projecting on ElementDG

Regarding https://github.com/kinnala/scikit-fem/discussions/895#discussioncomment-4044517 : I’ve made a minimal example showing a problem projecting on ElementDG:

import numpy as np
import matplotlib.pyplot as plt

from skfem import *

fig, axs = plt.subplots(1, 3, subplot_kw={'aspect': 1})

mesh = MeshTri().refined(4)

basis = Basis(mesh, ElementVector(ElementTriP1()))
x = basis.project(lambda x: np.array((x[1], -x[0])))
basis.plot(x, ax=axs[0])

basis2 = basis.with_element(ElementVector(ElementTriP1()))
x2 = basis2.project(basis.interpolate(x))
(x2_x, basis2_x), (x2_y, basis2_y) = basis2.split(x2)
basis2_x.plot(x2_x, ax=axs[1], shading='gouraud')

basis3 = basis.with_element(ElementVector(ElementDG(ElementTriP1())))
x3 = basis3.project(basis.interpolate(x))
(x3_x, basis3_x), (x3_y, basis3_y) = basis3.split(x3)
basis3_x.plot(x3_x, ax=axs[2], shading='gouraud')

plt.show()

[kinnala]

This looks better:

[HelgeGehring]

Okay, thanks!