Russian forces have made rapid gains in the eastern Donetsk region over the past week or so, capturing a few villages and closing in on the city of Pokrovsk, one of the main Ukrainian defensive strongholds in the area.

Russian forces are now only a dozen miles from Pokrovsk after Moscow’s troops pushed along a railway line and advanced about three miles toward the city, according to open-source maps of the battlefield based on combat footage and satellite imagery. The Russian progress contrasts sharply with the slow but steady gains that Moscow had made so far this year in the Donetsk region, sometimes measured in only a few hundred yards a week.

Military analysts say the swift gains reflect Moscow’s improved ability to exploit cracks in Ukrainian defensive lines, which have been thinned by manpower shortages and strained by relentless Russian attacks along a more than 600-mile front.

In recent months, the experts say, Russian forces have increasingly focused on identifying weakened and poorly organized Ukrainian units before breaking through by throwing scores of troops and armored vehicles onto the battlefield.

“Russians probe the lines to see if a battalion holds or retreats,” said Mykola Bielieskov, a military analyst at the government-run National Institute for Strategic Studies in Ukraine. Once they “find weakened battalions and brigades,” he added, “they press them no matter the losses.”