The Ukrainian forces are in the countryside all about, dug into positions in the open steppe. In their trenches and armored vehicles, they are all but impervious to even the most intensive rebel shelling.

“If one side shoots from one place, then their opponent will shoot back at that place,” Dr. Gennady M. Buniyev, the director of a trauma ward here, said, choosing his words carefully and insisting on his neutrality in the conflict, as the windows of his office shook from outgoing rounds.

The mortar crew operating inside the city in areas controlled by the Luhansk People’s Republic, a separatist group, was firing from just outside the walls of the hospital grounds.

In response this week, two rockets fired from Ukrainian-held territory smashed into the hospital yard, landing near a maternity ward and a storage shed for oxygen bottles. Fortunately, the oxygen did not ignite.

“If it blew up, the whole hospital would have gone with it,” Dr. Buniyev said.

In the afternoon on a main street, where heat shimmered off the pavement and artillery boomed all about, the only vehicle in sight was a taxi creeping along with a driver so nervous he later simply abandoned his passengers on a side road, leaving them to walk to a hotel that lacked electricity and water and any other guests.

Dr. Buniyev’s clinic was treating 16 people for shrapnel wounds, including one man with a gaping head wound and four patients with brain trauma from blast waves.

A bucket brigade carried water to the hospital; nurses boiled water on a wood fire in the yard.

Vladimir Demidenko, a surgeon, said trying to shoo away the mortar crew would be pointless. “They wouldn’t listen to us,” he said. “If we went to complain to them, they would kill us.”