Plotting subspaces of a mesh

Question

1) Is it possible to plot n-1 dimensional subspace of n-dimensional mesh?
2) Is it possible to plot only a part of the mesh with certain scalar mesh function greater or smaller than x?

Answer 1

1) You can use functions such as BoundaryMesh or SubMesh to define your n-1 dimensional mesh on which you then can define a new functionspace. You can interpolate or project functions from your n-dimensional functionspace onto your new n-1 dimensional one.
2) You can define a MeshFunction that is 1 or 0, depending on the comparison of your scalar function with x, and then use this MeshFunction to define a new SubMesh. This will work if you scalar function is piecewise constant (edit: within every element). If this is not the case, i.e. your scalar function equals x somewhere mid-element, you essentially need a new mesh, so I wouldn't know how to do it. If your goal is just to plot however (not to continue working on this new mesh), you can use a visualization program such as Paraview and clip above/below a certain value.

Comments

Is there any possibility of implementing 4th and higher dimensional elements? Actually for space-time analysis - 3D x TIME?

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There are some tutorials on time-dependent problems in the documentation here
http://fenicsproject.org/documentation/

If you mean treating space and time on the same footing, then you better post it as a new question, because I cannot help you there.