diff --git a/Solver/TESTCASES/Maxwell.lua b/Solver/TESTCASES/Maxwell.lua
new file mode 100644
index 0000000000000000000000000000000000000000..04ee26c41f323a7f09bddc8de7aebfd258859254
--- /dev/null
+++ b/Solver/TESTCASES/Maxwell.lua
@@ -0,0 +1,95 @@
+model = GModel  ()
+
+model:load ('box_maxwell.geo')
+model:load ('box_maxwell.msh')
+dg = dgSystemOfEquations (model)
+dg:setOrder(1)
+
+
+
+function valueOutlet(xyz, f)
+  for i=0,xyz:size1()-1 do
+    X = xyz:get(i,0)
+    Y = xyz:get(i,1)
+    Z = xyz:get(i,2)
+    VALUE1= math.sqrt(X*X+Y*Y)  
+    f:set(i,0,0)
+    f:set(i,1,0)
+    f:set(i,2,0)
+    f:set(i,3,0)
+    f:set(i,4,0)
+    f:set(i,5,0)
+  end
+end
+
+
+function valueInlet(xyz, f)
+  for i=0,xyz:size1()-1 do
+    X = xyz:get(i,0)
+    Y = xyz:get(i,1)
+    Z = xyz:get(i,2)
+    VALUE1= math.sqrt(X*X+Y*Y)
+    f:set(i,0,0)
+    f:set(i,2,0)
+    f:set(i,1,0*math.exp(-50*(z^2)))
+    f:set(i,3,0)
+    f:set(i,4,0)
+    f:set(i,5,0)
+  end
+end
+
+
+mu_eps=fullMatrix(6,1)
+mu_eps:set(0,0,1)
+mu_eps:set(1,0,1)
+mu_eps:set(2,0,1)
+mu_eps:set(3,0,1)
+mu_eps:set(4,0,1)
+mu_eps:set(5,0,1)
+law = dgConservationLawMaxwell(functionConstant(mu_eps):getName())
+dg:setConservationLaw(law)
+
+
+-- box-----
+outletFunction=functionLua(6,'valueOutlet',{'XYZ'}):getName()
+inletFunction=functionLua(6,'valueInlet',{'XYZ'}):getName()
+
+law:addBoundaryCondition('wall',law:newBoundaryWall())
+law:addBoundaryCondition('symmetry',law:newBoundaryWall())
+
+law:addBoundaryCondition('inlet',law:newSymmetryBoundary())
+law:addBoundaryCondition('outlet',law:newSymmetryBoundary())
+
+
+dg:setup()
+
+-- initial condition
+function initial_condition( xyz , f )
+  for i=0,xyz:size1()-1 do
+    x = xyz:get(i,0)
+    y = xyz:get(i,1)
+    z = xyz:get(i,2)
+    f:set (i, 0,0)
+    f:set (i, 1,0)
+    f:set (i, 2,math.exp(-50*((x-0.3)^2+(y-0.3)^2)))
+    f:set (i, 3,0) 
+    f:set (i, 4,0*math.cos(math.pi*x)) 
+    f:set (i, 5,0) 
+  end
+end
+dg:L2Projection(functionLua(6,'initial_condition',{'XYZ'}):getName())
+
+dg:exportSolution('output/MaxW-00000')
+
+dt=0.00075
+n=50
+
+-- main loop
+for i=1,3000 do
+ norm =  dg:RK44(dt)  
+  --t=t+dt
+  if (i % n == 0) then 
+    print('iter',i,norm)
+    dg:exportSolution(string.format("output/MaxW-%05d",i)) 
+  end
+end