approach to vertex fillet edge filling

Hello guys, I'm looking for an approach to create  multiple fillet edges that will be able to take care of the areas around the vertex (as highlighted in red). basically to smooth it. using traditional fillet edge of course does not work on filling the gaps around the vertex/ I know there are some mesh smoothing algorithms, or maybe build a minimal surface  around the edges.. I'm wondering if there is a standard for this procedure, perhaps in polygon modeling.. I'm more interested in the result than the format. thanks.