Gaps in surface

When I fillet the edge of this surface there appears to be gaps between the edge of the new fillet and the original surface within both the 3D model and the render. I was wondering if anyone might know the cause of this problem and some possible solutions please.

i had similar issues as well. I have been told there is problem with some display mesher which is not very good inside rhino. Try ClearAllmeshes command or explode the polysurface and join together

The cause is the mesh used for the display is too coarse for the curved edges to appear as smooth. The fix is to change the settings which are used by Rhino when creating dispaly meshes. DocumentProperties > Mesh.
If the setting is “Jagged and faster” try “Smooth and slower”
If the setting is “Smooth and slower” see the link below for suggestions of custom settings to use.

For more information see:

Thank you both for taking the time to provide your feedback on this topic.

I discovered that increasing the width of the horizontal flat surface where the two fillets meet removes the gaps in the rendered mesh.