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I need to manage the mesh size for finite element method solution to a differential equation, where properties change over two regions. This is for one dimension. I created a boundary mesh of three points to create two linear regions.

<< NDSolve`FEM`  

 bmesh = ToBoundaryMesh["Coordinates" -> {{0}, {2}, {4}},   
"BoundaryElements" -> {PointElement[{{1}, {2}, {3}}, {1, 1, 3}]},   
"PointElements" -> {PointElement[{{1}, {2}, {3}}, {1, 1, 3}]}]; 



 m3 = ToElementMesh[bmesh, "RegionMarker" -> {{{1}, 1, 0.2}, {{2}, 
 2, 0.05}}]


 m3["MeshElements"]

 m3["Coordinates"]

When I check the element coordinates, the second region does not seem to have the element spacing that I requested. I should be 0.05, but it seems to stay at 0.2.

Table[{m3["Coordinates"][[i]], i}, {i,1,Length[m3["Coordinates"]]}]

m3["Wireframe"["MeshElementIDStyle" -> Red]]

Can anyone help?

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    $\begingroup$ When you define m3, use { {3}, 2, 0.05} }. That is, the marker should be 3 instead of 2. $\endgroup$
    – LouisB
    Aug 20, 2019 at 23:20

1 Answer 1

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As pointed out in the comments the coordinate for the region marker needs to be within the region and not on the boundary of the region. This works:

m3 = ToElementMesh[bmesh, 
  "RegionMarker" -> {{{1}, 1, 0.2}, {{3}, 2, 0.05}}]
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