Howard Mitchell returns to the National Symphony Orchestra this week with a notable program. Roussel's "Bacchus et Ariane" Suite opens the program, to be followed by the Brahams Violin Concerto, with Itzhak Periman as soloist. The Eighth Symphony of Vaughan Williams will follow the Brahms. The program is being played tonight, Wednesday, and Thursday nights, and Friday afternoon.

The National Endowment for the Arts has announced plans for the 12th summer intern program. Nancy Hanks, chairman of the Endowment, said of the program, "The young people selected for the program represent a new generation of arts managers. Based on their records, the future looks very promising." The deadline for applications is March 4, 1977. For details, write Kathleen Bannon, Intern Program Officer, National Endowment For the Arts, Washington, D.C., 20506.

The Endowment has also announced a new assistant director of its music program. He is Adrian Gnam, who replaces Ralph Rizzolo, who resigned the post to become manager of the Phoenix Symphony. Gnam, who was born in Jefferson Valley, N.Y., is an oboist and conductor who has been, since 1970, director of university orchestras at Ohio University.

Coming Events: Andre Bernard, trumpet, with Rejean Poirier, organist, will play a free recital at 8 p.m. this Friday in the Shrine of the Immaculate Conception. At 8:30 that same evening clarinetist Sydney Forrest, cellist John Martin, and pianist Cary Lewis will play in the Library will include Beethoven, Berg, Brahms, and Pederecki.

The Montgomery County Master works Chorus, under the direction of Roger Ames, will sing Honegger's "King David," at 8 p.m. Saturday in Westmoreland Congregational soloist will be Ellen Lang, Michael Church. With narrators Jerry Whidden and Irene Crist and orchestra, the Hume, and Georgine Resick. Tickets at the door.