From https://docs.mongodb.com/manual/reference/operator/update/positional-filtered/#up.S[%3Cidentifier%3E]
Given the following collection
{
\"_id\" :
You can try below c# using both BsonDocument
and json string option. There is no linq option.
var filter = Builders<BsonDocument>.Filter.Empty;
var update = Builders<BsonDocument>.Update.Set("grades.$[elem].mean", 100);
var arrayFilter = new BsonDocumentArrayFilterDefinition<BsonDocument>(new BsonDocument("elem.grade", new BsonDocument("$gte", 85)));
var arrayFilter = new JsonArrayFilterDefinition<BsonDocument>("{ \"elem.grade\": { $gte: 85 } }");
var arrayFilters = new List<ArrayFilterDefinition> { arrayFilter };
var updateOptions = new UpdateOptions();
updateOptions.ArrayFilters = arrayFilters;
var result = collection.UpdateOne(filter, update, updateOptions);