From BiblePortal Wikipedia

Hawker's Poor Man's Concordance And Dictionary [1]

We meet with this name,  Isaiah 15:8. But it is more than probable, that it is the name of well so sweetly spoken of  Numbers 21:16-18. I beg the reader to consult the Scripture, and let him judge for himself, whether it be not so. Beerelim means, the well of the princes. And the princes are said to have digged it. But when the reader hath satisfied his mind on this point, there is another object, and that of an higher nature, that I would request the reader to attend to. In those wells, I humbly conceive, we discover gospel lessons beautifully represented. Hence, the prophet sings, "Because God (saith he) is my salvation, therefore, with joy shall ye draw water out of those wells of salvation." ( Isaiah 12:2-3) And hence, if, with an eye to the Lord Jesus Christ, who is himself, in the souls of all his redeemed, a well of water springing up unto everlasting life, ( John 4:14) we accept those Beer-elim in the word, we then join the Lord's song, in the Lord's own words, as he directed Moses. This is the well whereof the Lord spake unto Moses, "Gather the people together, and I will give them water." Then Israel sang this song. "Spring up, O well! sing ye unto it. The princes digged the well; the nobles of the people digged it, by the direction of the lawgiver with their staves." ( Numbers 21:16-18)

Holman Bible Dictionary [2]

 Isaiah 15:8 Numbers 21:16

Easton's Bible Dictionary [3]

 Numbers 21:16 Isaiah 15:8

Hastings' Dictionary of the Bible [4]

Beer-Elim . See Beer.

Cyclopedia of Biblical, Theological and Ecclesiastical Literature [5]

(Heb. Beer'E'im', בְּאֵר אֵלִים , Well Of Heroes; Sept. Τὸ Φρέαρ Τοῦ Αἰλείμ ; Vulg. Puteus Elim ) , a spot named in  Isaiah 15:8, as on the "border of Moab," apparently the south, Eglaim being at the north end of the Dead Sea. The name points to the well dug by the chiefs of Israel on their approach to the promised land, close by the "border of Moab" ( Numbers 21:16; comp.  Numbers 21:13), and such is the suggestion of Gesenius ( Jesaia. p. 533). (See Beer) simply. Beer-Elim was probably chosen by the prophet out of other places on the boundary on account of the similarity between the sound of the name and that of יְלָלָה the "howling," which was to reach even to that remote point (Ewald, Proph. p. 233).

International Standard Bible Encyclopedia [6]

- ẽr - ē´lim ( בּאר אלים , be'ēr 'ēlı̄m  ; φρέαρ τοῦ Ἀιλείμ , phréar toú Aileı́m , literally "well of Elim"): Probably lay to the North of Moab, answering to Eglaim in the South ( Isaiah 15:8 ). It may possibly be identical with Beer (1); but there is no certainty.