More from Chris Miller in Kyiv:
"The National Police of Ukraine reported this morning that they had received 71 allegations of election violations around the country. Most of them -- 10 -- were received in the eastern Donetsk region, with nine in the Dnipropetrovsk region, seven in the regions of Kharkiv Kyiv, six in Odesa Zaporizhye, and four in Luhansk, Sumy and Zakarpattia.
Police said that law enforcement had taken control of all polling stations where alleged violations occurred. Around 39,000 police officers are providing security at polling stations nationwide. In addition, reserves from the members of special forces police units and the National Guard are on standby in case of serious incidents."
Update from our correspondent on the ground, Christopher Miller (follow his Twitter here):
"Monitors at six polling stations in Kyiv's Podil district told RFE/RL that turnout before 10 a.m. seemed higher than previous elections and no falsifications had been reported. Police were on hand in the event of any irregularities, as were monitors representing various civil society organizations and political parties.
At School No. 9 the entire Dobriyvechir family of four voted for Volodymyr Zelenskyy, with daughter Anastasia, 19, saying she believed the comic-turned-candidate is a "good man" who shares the same values in real life as the fictional president he plays in his hit sitcom Servant of the People.
"He's going to make our country better" like he does in his show, she said. Her mother, Svitlana, said that Zelenskyy was the obvious choice for her, because life hasn't become better under incumbent President Petro Poroshenko. "Life has gotten worse in the past five years," she said. "Utility prices have gotten higher and pensioners like our grandmother can't afford to live."
"Poroshenko delivered visa-free travel and the Tomos" -- the declaration that created a new, independent Orthodox Church of Ukraine -- "but otherwise he didn't do enough for us," Svitlana added.
Tweet from the German ambassador to Ukraine: