He got to know a girl through the internet and he wants to marry her but her father is refusing
Question

I am a Muslim Arab youth. I got to know a Muslim girl of Arab origin who lives overseas, through the internet. It was – and still is – a relationship within the limits of the laws of Allaah, because, praise be to Allaah, I fear Allaah a great deal. I love her and she loves me because she is a committed Muslim girl, and she also fears Allaah. Our love is for the sake of Allaah, in sha Allaah. 
I proposed marriage to her, and she accepted and agreed, and I praised Allaah for answering my du’aa’ by blessing me with a righteous wife, especially since I have wanted to get married and settle down for a number of years. She told her mother, who is a non-Arab, and she agreed at first, because her father had been away from them from a while. Her father recently returned, and she was happy, but he had come to tell his daughter to get ready to marry a man from her father’s country, without asking his daughter’s opinion of the prospective groom. She is afraid of him because he beats her sometimes, and she sometimes says that he is crazy; may Allaah guide us and him. 
She told me that she does not want to marry this man and that she wants to marry me, and I told her the same thing. She said to me: What do you think of marrying me in secret, then we tell her father what has happened. She is over 18 years of age.
Praise be to Allah.You should note that Allaah sees and knows all that you do. 
“Allaah knows the fraud of the eyes, and all that the breasts conceal”
[Ghaafir 40:19 – interpretation of the meaning]
You should also note that you have done something that is not permissible according to sharee’ah, which is corresponding and speaking to one another. You have seen how the relationship between you developed until the Shaytaan was able to deceive you and make your relationship appear to you to be “love for the sake of Allaah”. 
Secondly: 
We know that love is the matter of the heart, and that a person is not to be blamed for that over which he has no control. But he is to be blamed fully for the things that led him to enter into this relationship, such as forbidden glances, or words spoken in secret over the phone or via the internet, and other footsteps of the Shaytaan which he wants to people to follow and fall into evil ways. Allaah says (interpretation of the meaning): 
“O you who believe! Follow not the footsteps of Shaytaan (Satan). And whosoever follows the footsteps of Shaytaan (Satan), then, verily, he commands Al-Fahsha’ [i.e. to commit indecency (illegal sexual intercourse)], and Al-Munkar [disbelief and polytheism (i.e. to do evil and wicked deeds; and to speak or to do what is forbidden in Islam)]. And had it not been for the Grace of Allaah and His Mercy on you, not one of you would ever have been pure from sins. But Allaah purifies (guides to Islam) whom He wills, and Allaah is All-Hearer, All-Knower”
[al-Noor 24:21]
He is also to be blamed for getting carried away in a matter in which the beginning is haraam and the end of which is an invalid marriage. 
But it has gone this far, and the relationship between you has reached the stage that you describe, so now it is up to the girl and her family. If the woman can convince her father not to marry her off to someone whom she dislikes, and she and her mother can convince him to let her marry you, and she is – as you say – qualified for marriage, then you should follow the steps outlined in sharee’ah of asking her father or her guardian for her hand in marriage. If you see that the path to marriage is blocked, then it is not permissible for you to carry on with this relationship. Whoever gives up something for the sake of Allaah, Allaah will compensate him with something better than it. It may be better for her to marry someone other than you, and it may be better for you to marry someone other than her. 
“and it may be that you dislike a thing which is good for you and that you like a thing which is bad for you. Allaah knows but you do not know”
[al-Baqarah 2:216 – interpretation of the meaning]
If what this girl says about her father is true and he is insane – but we do not think that he really is insane in the sense that his rights of shar’i guardianship over her are waived and he is not fit to take charge of the affairs of his dependents – or he is denying her the right to marry one who is compatible with no legitimate shar’i excuse, then in that case the role of guardian is transferred to the next closest guardian, so it moves from the father to the grandfather, for example. This matter is discussed in detail in the answer to question no. 7193. 
As for thinking of getting married in secret, without her guardian’s permission, this will only make matters even worse. May Allaah protect us and you from the causes of His wrath and punishment. 
Do you not know that the Prophet (peace and blessings of Allaah be upon him) said: “Any woman who gets married without the permission of her guardian, her marriage is invalid,” three times. Narrated by Abu Dawood, 2083; classed as saheeh by al-Albaani in Saheeh Abi Dawood. So how can you think of this invalid marriage that is not pleasing to Allaah and His Messenger, and then claim that your love is for the sake of Allaah? 
Do you not know that the Prophet (peace and blessings of Allaah be upon him) commanded that marriages be announced publicly? He said: “Announce marriages publicly.” Narrated by Ahmad from the hadeeth of ‘Abd-Allaah ibn al-Zubayr. Al-Albaani said: (it is) hasan. 
He made this public announcement the factor that distinguishes a halaal marriage from haraam fornication, and said: “What distinguishes between haraam and halaal is the daff and voices (raised in song).” Narrated by al-Tirmidhi, 1088; classed as hasan by al-Albaani in Saheeh al-Tirmidhi. 
Imam al-Baaji (may Allaah have mercy on him) said in Sharh al-Muwatta’: There is no dissent concerning the fact that marriage in secret is forbidden, because it is similar to zina which is also done in secret… hence it is prescribed to celebrate marriages and give wedding feasts, because that is a public announcement of the marriage. 
He also said:  Every marriage in which the witnesses are sworn to secrecy is a secret marriage, even if there are many witnesses. 
Look at what you two are claiming. Is it a permissible marriage as prescribed by Allaah and His Messenger, or it is the matter of whims and desires and zina, and the footsteps of the Shaytaan? 
Beware before you both slip and fall, and build your lives on a shaky foundation. May Allaah keep us and you safe from the Fire of Hell. 
But if the father of this girl wants to arrange her marriage against her wishes, neither the father nor any other guardian, has the right to force his daughter to marry someone she dislikes, as is explained in questions no. 26852, 7193, 22760.  But this is nothing to do with you, and you are not responsible for that. So leave her and her guardians alone. If is not decreed for you two to marry, and you withdraw from her life, as is required of you in that case, then perhaps she will see that this suitor or someone else is the right husband for her. May Allaah make us and you rich (independent of means) by His bounty. And Allaah is the Source of strength.