Update statement to set a column based the maximum row of another table

I have a Family table:

SELECT * FROM Family;

id | Surname  | Oldest
---+----------+------
 1 | Byre     | NULL
 2 | Summers  | NULL
 3 | White    | NULL
 4 | Anders   | NULL

The Family.Oldest column is not yet populated. There is another table of Children:

SELECT * FROM Children;

id | Name     | Age  | Family_FK
---+----------+------+--------
 1 | Jake     | 8    | 1
 2 | Martin   | 7    | 2
 3 | Sarah    | 10   | 1
 4 | Tracy    | 12   | 3

where many children (or no children) can be associated with one family. I would like to populate the Oldest column using an UPDATE ... SET ... statement that sets it to the Name of the oldest child in each family. Finding the name of each oldest child is a problem that is solved quite well here: How can I SELECT rows with MAX(Column value), DISTINCT by another column in SQL?

However, I don't know how to use the result of this in an UPDATE statement to update the column of an associated table using the h2 database.