fem complete

example/Burgers_FEM/Project.toml

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+name = "Burgers_FEM"
+uuid = "e5170f7b-8a26-429b-971b-688deff48327"
+authors = ["Yueh-Hua Tu"]
+version = "0.1.0"
+
+[deps]
+FEniCS = "186dfeec-b415-5c13-8e76-5fbf19f56f9b"
+OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"
+
+[compat]
+julia = "1.6"
+
+[extras]
+Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+
+[targets]
+test = ["Test"]

example/Burgers_FEM/README.md

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+# Burgers_FEM
+
+[![Stable](https://img.shields.io/badge/docs-stable-blue.svg)](https://yuehhua.github.io/Burgers_FEM.jl/stable)
+[![Dev](https://img.shields.io/badge/docs-dev-blue.svg)](https://yuehhua.github.io/Burgers_FEM.jl/dev)
+[![Build Status](https://github.com/yuehhua/Burgers_FEM.jl/actions/workflows/CI.yml/badge.svg?branch=main)](https://github.com/yuehhua/Burgers_FEM.jl/actions/workflows/CI.yml?query=branch%3Amain)
+[![Coverage](https://codecov.io/gh/yuehhua/Burgers_FEM.jl/branch/main/graph/badge.svg)](https://codecov.io/gh/yuehhua/Burgers_FEM.jl)

example/Burgers_FEM/src/Burgers_FEM.jl

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+module Burgers_FEM
+
+using FEniCS
+
+function run_fem(ν=1/1000)
+    # parameters
+    s = 1024  # x
+    steps = 200  # t
+
+    DT = Constant(1/steps)
+    dt = 1/steps
+
+    mesh = UnitIntervalMesh(s)
+    V = FunctionSpace(mesh, "CG", 1)
+
+    bc = DirichletBC(V, 0., "on_boundary")
+
+    u_init = Expression("x[0]", degree=1)
+    u = TrialFunction(V)
+    u_old = FeFunction(V)
+    v = TestFunction(V)
+
+    u = interpolate(u_init, V)
+    assign(u_old, u)
+
+    f = Expression("0.0", degree=0)
+
+    F = (dot(u - u_old, v) / DT
+        + ν*inner(grad(u), grad(v))
+        + inner(u*directional_derivative(u, 0), v)
+        - dot(f, v)
+    )*dx
+
+    us = Vector{Float64}[]
+    t = 0.0
+    for n in 1:steps
+        t = t + dt
+        nlvsolve(F, u, bc)
+        push!(us, get_array(u))
+        assign(u_old, u)
+    end
+
+    return us
+end
+
+end

example/Burgers_FEM/test/runtests.jl

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+using Burgers_FEM
+using Test
+
+@testset "Burgers_FEM.jl" begin
+    # Write your tests here.
+end