# FEM Meshrefinement for 1D Interval and Elements of order 2

I would like to create a 1D mesh of the intervall (-pi/2,pi/2) for solving a DE with FEM, with more elements close to +-1 - these elements should be of order 2, since order 1 elements yield too low accuracy.

For the function ToElementMesh the option "MeshRefinementFunction" does not work in 1D, which is why I tried to first use the function Discretize region and convert the result a FEM mesh, this gives the wrong answer though:

Needs["NDSolveFEM"];
A = ImplicitRegion[True, {{x, -\[Pi]/2, \[Pi]/2}}];
f = Function[{vertices, area},
area > 0.01 (1 + 10*Abs[(Norm[Mean[vertices]] - 1)])];
B = DiscretizeRegion[A, MeshRefinementFunction -> f]

Z = ToElementMesh[B]
ElementMesh[{{-1.5708, 4.63385}}, {LineElement["<" 159 ">"]}]


The resulting mesh goes from -pi/2 to ~4.6 and not to pi/2 as it should be. Is there any way to get this to work? Thanks in advance.

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## 1 Answer

Hm, smells like a bug. You can use this in the mean time:

MeshOrderAlteration[B["MakeRepresentation"["ElementMesh"]], 2]

• This gives me just what I needed, thanks a lot!
– Eddi
Sep 30, 2021 at 8:49