A poem expressing sadness, especially for somebody who is dead, is known as a/an-

- Elegy is a Lyric poem mourning for the death of an individual or lamenting over a tragic event.
- Tragedy is a form of drama which presents the fall of a superior human being for a mistake of some kind.
- A sonnet is a lyric poem of fourteen iambic pentameter lines.
- Lyric is a short poem expressing personal or subjective thoughts and intense feelings of a single speaker.
- It is identical to a song sung with a lyre.
Source: An ABC of English Literature, Dr. M Mofizar Rahman.