Is this realistic at all? It does not seem possible

Apparently, YES

There's a long article at Vulture.com which goes into the physics and math but essentially (movie magic aside)... the actual "jump" is possible. The landing...probaly not so much.

The Lykan HyperSport weighs a little over 3,000 pounds. (With the two actors in it, it would probably weigh around 3,400 pounds.) Using Google Earth, we estimate the distance between the towers to be anywhere between 140 and 170 feet — so we’re going to approximate the distance they need to jump to be about 150 feet. (The third tower they jump to seems like it might be a bit farther, but we’ll assume a uniform distance for the sake of this calculation. We’re also assuming zero wind resistance, because there’s no way to ascertain what the wind resistance on a fictional day in a fictional movie might be. Also, at these distances, wind resistance probably wouldn’t make much difference.)

“There is no one shot showing the entire flight, so exactly how far the car falls is hard to determine,” says Loveridge. “It is certainly at least two stories, or about 20 feet, but I don’t think it could be more than four stories.”

“For a four-story fall, the car should be moving at an angle of about 35 degrees when it hits the building, but in the film, it seems to be tilted at only 12 degrees. If this were the case, you would clearly see the back end drop below the landing floor before reaching it, which is not how it is portrayed. If the car dropped only two stories, the expected landing angle is about 18 degrees, which is much closer to the 12-degree angle they show and could be within the expected errors of such a calculation.

“Falling four stories takes about 1.6 seconds, while falling two takes only about 1.1 seconds. To cover the necessary 150 feet in this time, the car would have to be traveling about 70 miles per hour if it falls four stories, or about 100 miles per hour to only fall two stories. Both of these speeds are clearly achievable by this car.”

The effect is almost entirely CGI.

There’s ambitious and then there’s just plain unsafe. That’s a line the filmmakers were not even going to come close to crossing.

“You’re not ever jumping a car from a real building,” Gill acknowledges.

So, if the team couldn’t jump a car from building to building of the Etihad Towers in Abu Dhabi, they did the next best thing.

They built 40 foot tall glass and steel enclosures inside a giant sound stage in Atlanta. Once that was complete, a stunt driver crashed at high speed through each “tower.”

While most of the stunts are done by stunt professionals, Kramer was quick to point out that Paul Walker and Vin Diesel were more than capable of handling those duties.

^Source

Well, it all depends on the car speed, which is no question for the Lykan Hypersport !! Also, please note that the car always jumps at a floor lower than the previous building, so yes, filmmakers and director have kept in mind the laws of physics and logic !!