amicable, uncontested
no-fault
acrimonious, bitter, messy, nasty, painful, ugly
quick, quickie (informal)
parental
Parental divorce can have lasting negative consequences for children.

civil
The church may disapprove but Catholics can and do obtain civil divorces.

want
apply for, ask for, file for, petition for, seek, sue for
She filed for divorce in 1996.

initiate
The majority of divorces are initiated by women.

get, have, obtain
He told her that he was married but getting a divorce.

experience, go through
She watched her parents go through an acrimonious divorce.

agree to, consent to
contest
These days divorce is rarely contested.

finalize
Once the divorce is finalized, I plan to move to Bermuda.

handle
the lawyers handling their divorce

grant (sb)
Over 50 000 divorces were granted last year.

end in
An increasing number of marriages end in divorce.

consider
Neither partner had considered divorce.

come through
He is waiting for the divorce to come through before he remarries.

court
case, proceedings, process
petition
papers
He hasn't signed the divorce papers yet.

decree, settlement
figures, rate, statistics
The divorce rate has been growing steadily since 1971.

law
attorney (AmE), lawyer
mediation

divorce from
her divorce from the star

divorce on the grounds of
She is seeking a divorce on the grounds of cruelty.

grounds for divorce
He cited adultery as grounds for divorce.

Divorce is used with these nouns as the object:
husband