This is Islamic Sharia Law being applied in Sudan. As Robert Spencer notes in his coverage of this case:
Islamic apologists in the West routinely claim that Islam has no death penalty for apostasy. Unfortunately, misunderstanders of Islam abound in large numbers, and for some reason they cannot shake the notion that Islam does mandate death for those who are considered to have left the faith.
Why do they persist in this misunderstanding? Maybe it’s because Muhammad commanded: “Whoever changed his Islamic religion, then kill him” (Bukhari 9.84.57). This is still the position of all the schools of Islamic jurisprudence, both Sunni and Shi’ite.
Sheikh Yusuf al-Qaradawi, the most renowned and prominent Muslim cleric in the world, has stated: “The Muslim jurists are unanimous that apostates must be punished, yet they differ as to determining the kind of punishment to be inflicted upon them. The majority of them, including the four main schools of jurisprudence (Hanafi, Maliki, Shafi`i, and Hanbali) as well as the other four schools of jurisprudence (the four Shiite schools of Az-Zaidiyyah, Al-Ithna-`ashriyyah, Al-Ja`fariyyah, and Az-Zaheriyyah) agree that apostates must be executed.”
Pregnant Woman Facing Execution in Sudan: 'I am a Christian'
by Frances Martel, Breitbart News — May 15, 2015
Mariam Yahia Ibrahim Ishag, a 27-year-old pregnant mother, has been sentenced to death in Sudan for "apostasy" for marrying a Christian, despite being raised a Christian, because her father was Muslim. Ibrahim has refused to accept Islam after a three-day stay on her execution and is slated to be killed today.
Ibrahim, who is almost nine months pregnant, is married to an American citizen of South Sudanese descent, who has applied for her to come to the United States but has not yet received approval from the American government. Her marriage is considered void by the Sudanese government because of her husband's Christian faith, and she was sentenced to hanging and 100 lashes for both adultery and apostasy. She was given three days to abandon the Christian faith and her husband and children-- her unborn child and an 18-month-old boy-- and "revert" to her father's religion. The court did not make clear what would happen to the children should she renounce Christianity-- and thus her family-- and accept their version of Islam.
Ibrahim refused to abandon her religious faith, telling the judge, "I am a Christian and I never committed apostasy."
"We gave you three days to recant but you insist on not returning to Islam," Judge Abbas Mohammed Al-Khalifa told her, according to Al Jazeera, announcing his death sentence and the additional lashes for "adultery." The judge only addressed her by her father's name, emphasizing his Muslim background.
Ibrahim's attorneys have said that they will seek to overturn the sentence at a higher court. One attorney told AFP they "very much hope that this will be corrected on appeal," and that they believe the ruling to be unconstitutional. While Sudan's government operates under Sharia law, this execution is considered a uniquely harsh sentence in the country. Sudanese law does not allow Muslim women to marry outside of their faith. Men may marry outside of their faith, but the law demands their children be raised Muslim.
Witnesses note that the death sentence was met with a small group of protesters calling for her release, and one protester in particular calling for an organized sit-in campaign until Ibrahim is released. Activists also called the decision a case of "blatant interference in the personal life of Sudanese citizens."
Amnesty International also issued a statement, calling the decision "abhorrent": "The fact that a woman has been sentenced to death for her religious choice, and to flogging for being married to a man of an allegedly different religion, is appalling and abhorrent... adultery and apostasy are acts which should not be considered crimes at all."
As the sentence has just been handed down, there is not yet a report on when Ibrahim is scheduled to be hanged.