It appears that the offensive against Mariupol is beginning again in earnest, since there was a lot of shelling in the city's outskirts over the weekend
Probably the worst place to stir up trouble, as the more militant Avoz Battalion is based in that area and far more likely to engage head on.
It is quite possible that this is just an aggressive response to earlier shelling in one direction or the other. The latest OSCE report indicates that there has been sporadic shelling over the last few days in that area, in both directions, although there is no clear 'front' so it is difficult to say for sure who was firing:
"On 15 August, in "DPR"-controlled Krasnoarmiiske (33km north-east of Mariupol) the SMM conducted crater analyses of eight fresh craters. According to a "DPR" member present, the shelling took place on 14 August. The SMM concluded that they were all caused by Grad multiple launch rocket systems (MLRS, 122mm) originating from a westerly direction.
On the same day in government-controlled Andriivka (41km north-north-east of Mariupol), the SMM conducted crater analysis of eleven fresh craters caused by shelling on the previous day, according to information received from a resident. The SMM assessed that the impacts have been caused by 152mm artillery incoming from a north-easterly direction.
On 16 August the SMM visited "DPR"-controlled Telmanove (50km north-east of Mariupol) to follow up on reports by representatives of the Ukrainian Armed Forces at the JCCC that the village had been shelled in the early morning. The SMM analysed 16 craters and concluded that they were caused by MLRS (122mm BM-21 Grad) fired from a west-south-westerly direction."
This was allegedly on the 16th. 3 days later there appears to be no concerted follow up so I suspect it was just a single engagement rather than any attempt at assault.
However this is Mariupol's opinion on becomeing part of a break-away republic:
So I suspect there would be less of a welcome for a separatist force.
I suspect the Russians still want that land-bridge to Crimea, though some here think that may be too heavy a lift.
Putin is slowly distancing himself from the situation, militarily. He has stirred up trouble and left that pot to simmer, and now has bigger fish to fry (NATO in Poland, Estonia, Latvia, Lithuania, ISIS to the south). While the Russian military may be able to seize the 200+km of coast line that they would need to hold to secure a land-bridge, it is highly unlikely that a separatist force on its own could do so, and even less likely that they could sustain it.
That would drag Russia into the fight full on, and I don't think there is the political will or public support to go with that.
This is an attempt by the DPR to complete their stated intention and control the whole of the Donetsk and Lughansk oblasts, but the whole thing has lost momentum and has bogged down, with neither side really committed to full-on action.
Wonder how viable a bridge across the Kerch Strait would be?
It has been tried a couple of times in the past, without success, although technology has moved on. Medvedev has stated that it will be built, and the project is once again under way with an intended completion date of 2019: link
However the cost and logistics is pretty immense (The project is estimated to cost 228 billion rubles, or 4.36 billion USD) and I am not sure that Crimea is worth the expense, other than perhaps politically. Crimea is not self sustaining and what they really need is supplies (especially water) from Ukraine, but no way Ukraine is going to entertain that to land they deem illegally occupied.