Koranic verses indicate existence of the Purgatory
The following verses indicate divine punishment and divine reward in the Purgatory:
Do not reckon those who are killed for God’s sake (martyrdom) are dead, but rather [they are] living, they will be provided for by their Lord (3/169)
So happy will they be with whatever God had given them out of His bounty, and rejoicing for those they left behind who have not yet overtaken them.
No fear will fall on them nor will they be saddened (3/170)
The following verses confirm Resurrection:
When the sky will split open (84/1)
And listen to its Lord as it ought to (84/2)
When the sky burst apart (82/2)
When planets are strewn around (82/2)
When the sun has been extinguished (81/1)
When the stars slip out of place (82/2)
Some day the earth will be changed into different earth, and [so will] heaven, they will emerge for God Alone. The Irresistible! (14/48)
Some day mankind will act like scattered moths (101/4) and the mountains seem like tufts of yarn! (101/5)
On a day when the sky will be like molten brass (70/8)
And the mountains like tufts of yarn (70/9)
These verses present the signs of Resurrection but the previous in which the Hell and paradise (Garden ) are mentioned , all indicate the purgatory.
Sources :
"Recognition of Resurrection" (By Allameh Mohammad Hossein Tehrani)