How to filter array in subdocument with MongoDB

I have array in subdocument like this

{
    "_id" : ObjectId("512e28984815cbfcb21646a7"),
    "list" : [
        {
            "a" : 1
        },
        {
            "a" : 2
        },
        {
            "a" : 3
        },
        {
            "a" : 4
        },
        {
            "a" : 5
        }
    ]
}

Can I filter subdocument for a > 3

My expect result below

{
    "_id" : ObjectId("512e28984815cbfcb21646a7"),
    "list" : [
        {
            "a" : 4
        },
        {
            "a" : 5
        }
    ]
}

I try to use $elemMatch but returns the first matching element in the array

My query:

db.test.find( { _id : ObjectId("512e28984815cbfcb21646a7") }, { 
    list: { 
        $elemMatch: 
            { a: { $gt:3 } 
            } 
    } 
} )

The result return one element in array

{ "_id" : ObjectId("512e28984815cbfcb21646a7"), "list" : [ { "a" : 4 } ] }

and I try to use aggregate with $match but not work

db.test.aggregate({$match:{_id:ObjectId("512e28984815cbfcb21646a7"), 'list.a':{$gte:5}  }})

It's return all element in array

{
    "_id" : ObjectId("512e28984815cbfcb21646a7"),
    "list" : [
        {
            "a" : 1
        },
        {
            "a" : 2
        },
        {
            "a" : 3
        },
        {
            "a" : 4
        },
        {
            "a" : 5
        }
    ]
}

Can I filter element in array to get result as expect result?

Using aggregate is the right approach, but you need to $unwind the list array before applying the $match so that you can filter individual elements and then use $group to put it back together:

db.test.aggregate([
    { $match: {_id: ObjectId("512e28984815cbfcb21646a7")}},
    { $unwind: '$list'},
    { $match: {'list.a': {$gt: 3}}},
    { $group: {_id: '$_id', list: {$push: '$list.a'}}}
])

outputs:

{
  "result": [
    {
      "_id": ObjectId("512e28984815cbfcb21646a7"),
      "list": [
        4,
        5
      ]
    }
  ],
  "ok": 1
}

MongoDB 3.2 Update

Starting with the 3.2 release, you can use the new $filter aggregation operator to do this more efficiently by only including the list elements you want during a $project:

db.test.aggregate([
    { $match: {_id: ObjectId("512e28984815cbfcb21646a7")}},
    { $project: {
        list: {$filter: {
            input: '$list',
            as: 'item',
            cond: {$gt: ['$$item.a', 3]}
        }}
    }}
])

$and: get data between 0-5:

cond: { 
    $and: [
        { $gt: [ "$$item.a", 0 ] },
        { $lt: [ "$$item.a", 5 ] }
]}