From 5e289dd97832116c01b7e05a13648d084b3944ea Mon Sep 17 00:00:00 2001
From: Yueh-Hua Tu <a504082002@gmail.com>
Date: Sun, 17 Jul 2022 15:43:41 +0800
Subject: [PATCH] fem complete

update README and format
---
 example/Burgers_FEM/Project.toml       | 17 ++++++++++
 example/Burgers_FEM/README.md          |  9 +++++
 example/Burgers_FEM/src/Burgers_FEM.jl | 46 ++++++++++++++++++++++++++
 example/Burgers_FEM/test/runtests.jl   |  6 ++++
 test/runtests.jl                       |  1 +
 5 files changed, 79 insertions(+)
 create mode 100644 example/Burgers_FEM/Project.toml
 create mode 100644 example/Burgers_FEM/README.md
 create mode 100644 example/Burgers_FEM/src/Burgers_FEM.jl
 create mode 100644 example/Burgers_FEM/test/runtests.jl

diff --git a/example/Burgers_FEM/Project.toml b/example/Burgers_FEM/Project.toml
new file mode 100644
index 00000000..492413f0
--- /dev/null
+++ b/example/Burgers_FEM/Project.toml
@@ -0,0 +1,17 @@
+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"]
diff --git a/example/Burgers_FEM/README.md b/example/Burgers_FEM/README.md
new file mode 100644
index 00000000..abb1e741
--- /dev/null
+++ b/example/Burgers_FEM/README.md
@@ -0,0 +1,9 @@
+# Burgers' equation resolved by finite element method
+
+This example exhibits PDE problem for Burgers' equation resolved by finite element method. Change directory to `example/Burgers_FEM` and use following commend to solve the problem:
+
+```julia
+$ julia --proj
+
+julia> using Burgers_FEM; Burgers_FEM.run_fem()
+```
diff --git a/example/Burgers_FEM/src/Burgers_FEM.jl b/example/Burgers_FEM/src/Burgers_FEM.jl
new file mode 100644
index 00000000..54d0e83c
--- /dev/null
+++ b/example/Burgers_FEM/src/Burgers_FEM.jl
@@ -0,0 +1,46 @@
+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, 0.0, "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
diff --git a/example/Burgers_FEM/test/runtests.jl b/example/Burgers_FEM/test/runtests.jl
new file mode 100644
index 00000000..7ea9e5e8
--- /dev/null
+++ b/example/Burgers_FEM/test/runtests.jl
@@ -0,0 +1,6 @@
+using Burgers_FEM
+using Test
+
+@testset "Burgers_FEM.jl" begin
+    # Write your tests here.
+end
diff --git a/test/runtests.jl b/test/runtests.jl
index 6ffe561a..4fd870cf 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -27,3 +27,4 @@ end
     　l、ﾞ ~ヽ
     　じしf_, )ノ
 =#
+# Want some fish?