module PoissonDGTests

using Test

using Gridap

import Gridap: ∇

using Gridap.Geometry: DiscreteModelMock

model = DiscreteModelMock()

const h = 1

order = 2

const γ = 10

Ω = Triangulation(model)

Γ = BoundaryTriangulation(model)

Λ = SkeletonTriangulation(model)

degree = order

dΩ = Measure(Ω,degree)

dΓ = Measure(Γ,degree)

dΛ = Measure(Λ,degree)

n_Γ = get_normal_vector(Γ)

n_Λ = get_normal_vector(Λ)

u(x) = x[1]^2 + x[2]

∇u(x) = VectorValue( 2*x[1], one(x[2]) )

Δu(x) = 2

f(x) = - Δu(x)

∇(::typeof(u)) = ∇u

V = TestFESpace(model,ReferenceFE(lagrangian,Float64,order),conformity=:L2)

U = TrialFESpace(V,u)

a(u,v) =

∫( ∇(v)⋅∇(u) )*dΩ +

∫( (γ/h)*v*u - v*(n_Γ⋅∇(u)) - (n_Γ⋅∇(v))*u )*dΓ +

∫( (γ/h)*jump(v*n_Λ)⋅jump(u*n_Λ) - jump(v*n_Λ)⋅mean(∇(u)) - mean(∇(v))⋅jump(u*n_Λ) )*dΛ

l(v) =

∫( v*f )*dΩ +

∫( (γ/h)*v*u - (n_Γ⋅∇(v))*u )*dΓ

op = AffineFEOperator(a,l,U,V)

uh = solve(op)

e = u - uh

l2(u) = sqrt(sum( ∫( u⊙u )*dΩ ))

h1(u) = sqrt(sum( ∫( u⊙u + ∇(u)⊙∇(u) )*dΩ ))

el2 = l2(e)

eh1 = h1(e)

ul2 = l2(uh)

uh1 = h1(uh)

@test el2/ul2 < 1.e-8

@test eh1/uh1 < 1.e-7

end # module