Visualize PDE Solutions on a 3D Mesh 

Import a 3D mesh as a MeshRegion.

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X gc = Import[ "http://www.honda-3d.com/data/fuya-jo.zip", \ {"fuya-jo\\fuya-jo_LOW.stl", "GraphicsComplex"}]; bmr = BoundaryMeshRegion[First@gc, Last@gc]

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Solve a PDE over the imported region.

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X if = NDSolveValue[{Laplacian[u[x, y, z], {x, y, z}] == 1, DirichletCondition[u[x, y, z] == 10, z <= 1/2]}, u, {x, y, z} \[Element] bmr, Method -> {"PDEDiscretization" -> {"FiniteElement", "MeshOptions" -> {"MeshOrder" -> 1}}}]

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Now visualize the solution on the mesh.

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X vals = if @@ # & /@ First[gc]; {minVal, maxVal} = {Min[vals], Max[vals]}; colors = ColorData["TemperatureMap"][Rescale[#, {minVal, maxVal}]] & /@ vals;

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X Graphics3D[{EdgeForm[None], GraphicsComplex[First[gc], Last[gc], VertexColors -> colors]}, ViewPoint -> {40, 30, -10}, Boxed -> False]

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