is an option for DiscretizeRegion and related functions that specifies a function to indicate whether mesh cells should be refined or not.


  • With MeshRefinementFunction->f, the function f[vlist,m] is applied to each simplex created, where vlist is a list of the vertices and m is the measure. If f[vlist,m] returns True, the simplex will be refined.


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Basic Examples  (2)

Discretize a Disk so that the triangles near the center are smaller:

Discretize a Rectangle so that the triangles in the first quadrant are smaller:

Scope  (4)

MeshRefinementFunction specifies a function to determine if further refinement is needed:

Further refinement is performed on triangles for which the function returns True:

Using If makes it possible to refine triangles satisfying an implicit equation:

See the boundary between large and small triangles:

MeshRefinementFunction can be used with TriangulateMesh:

Triangulate it with smaller triangles near the lower-left corner:

MeshRefinementFunction can be used with DiscretizeRegion:

Discretize it with smaller triangles further away from the center:

Introduced in 2014