Analytical function: sum the cumulative of previous column

Using an analytical function, I want that the column 'sum' contains the cumulative of the previous column. But my code gets the total sum of all encounters. Here is both table and data for testing:

CREATE TABLE users (
  user_id INT PRIMARY KEY,
  name CHARACTER VARYING(50)
);

CREATE TABLE orders_catalog (
	order_code INT PRIMARY KEY,
	order_desc CHARACTER VARYING(50) NOT NULL,
	cost REAL NOT NULL
);

CREATE TABLE encounter (
	encounter_id INT PRIMARY KEY,
	user_id INT NOT NULL,
	encounter_type CHARACTER VARYING(50) NOT NULL,

	CONSTRAINT FK_encounter FOREIGN KEY (user_id) REFERENCES users(user_id)
);

CREATE TABLE orders (
	order_id INT PRIMARY KEY,
	order_code INT NOT NULL,
	encounter_id INT NOT NULL,
	created_dt TIMESTAMP NOT NULL DEFAULT CURRENT_TIMESTAMP,

	CONSTRAINT FK_orders_catalog FOREIGN KEY (order_code) REFERENCES orders_catalog (order_code),
	CONSTRAINT FK_orders_encounter FOREIGN KEY (encounter_id) REFERENCES encounter(encounter_id)
);
--

INSERT INTO users(user_id, name) VALUES(1, 'Peter');
INSERT INTO users(user_id, name) VALUES(2, 'Charles');
INSERT INTO users(user_id, name) VALUES(3, 'Eva') ;
INSERT INTO users(user_id, name) VALUES(4, 'John');
INSERT INTO users(user_id, name) VALUES(5, 'Helene');

INSERT INTO orders_catalog(order_code, order_desc, cost) VALUES (10000, 'Painting', 100.34);
INSERT INTO orders_catalog(order_code, order_desc, cost) VALUES (10001, 'Painting', 214.11);
INSERT INTO orders_catalog(order_code, order_desc, cost) VALUES (10002, 'Painting', 214.11);
INSERT INTO orders_catalog(order_code, order_desc, cost) VALUES (10003, 'Spare part', 181.03);
INSERT INTO orders_catalog(order_code, order_desc, cost) VALUES (10004, 'Sheet metal', 168.18);
INSERT INTO orders_catalog(order_code, order_desc, cost) VALUES (10005, 'Sheet metal', 240.02);
INSERT INTO orders_catalog(order_code, order_desc, cost) VALUES (10006, 'Sheet metal', 240.02);
INSERT INTO orders_catalog(order_code, order_desc, cost) VALUES (10007, 'Electricity', 146.85);
INSERT INTO orders_catalog(order_code, order_desc, cost) VALUES (10008, 'Spare part', 162.13);
INSERT INTO orders_catalog(order_code, order_desc, cost) VALUES (10009, 'Electricity', 140.02);
INSERT INTO orders_catalog(order_code, order_desc, cost) VALUES (10010, 'Electricity', 180.02);

INSERT INTO encounter(encounter_id, user_id, encounter_type) VALUES(100,1,'appointment');
INSERT INTO encounter(encounter_id, user_id, encounter_type) VALUES(101,2,'appointment');
INSERT INTO encounter(encounter_id, user_id, encounter_type) VALUES(102,3,'appointment');
INSERT INTO encounter(encounter_id, user_id, encounter_type) VALUES(103,4,'urgent');
INSERT INTO encounter(encounter_id, user_id, encounter_type) VALUES(104,5,'urgent');
INSERT INTO encounter(encounter_id, user_id, encounter_type) VALUES(105,1,'appointment');
INSERT INTO encounter(encounter_id, user_id, encounter_type) VALUES(106,2,'appointment');
INSERT INTO encounter(encounter_id, user_id, encounter_type) VALUES(107,3,'waiting');
INSERT INTO encounter(encounter_id, user_id, encounter_type) VALUES(108,4,'urgent');
INSERT INTO encounter(encounter_id, user_id, encounter_type) VALUES(109,5,'waiting');
INSERT INTO encounter(encounter_id, user_id, encounter_type) VALUES(110,1,'waiting');

INSERT INTO orders(order_id, order_code, encounter_id, created_dt) VALUES (1000,10000,100,'2009-06-16 09:12');
INSERT INTO orders(order_id, order_code, encounter_id, created_dt) VALUES (1001,10001,101,'2009-06-16 09:12');
INSERT INTO orders(order_id, order_code, encounter_id, created_dt) VALUES (1002,10002,102,'2009-06-16 09:12');
INSERT INTO orders(order_id, order_code, encounter_id, created_dt) VALUES (1003,10003,103,'2009-12-03 09:50');
INSERT INTO orders(order_id, order_code, encounter_id, created_dt) VALUES (1004,10004,104,'2010-02-24 12:21');
INSERT INTO orders(order_id, order_code, encounter_id, created_dt) VALUES (1005,10005,105,'2010-03-27 23:54');
INSERT INTO orders(order_id, order_code, encounter_id, created_dt) VALUES (1006,10006,106,'2010-03-22 12:43');
INSERT INTO orders(order_id, order_code, encounter_id, created_dt) VALUES (1007,10007,107,'2010-02-24 12:21');
INSERT INTO orders(order_id, order_code, encounter_id, created_dt) VALUES (1008,10008,108,'2010-03-04 08:55');
INSERT INTO orders(order_id, order_code, encounter_id, created_dt) VALUES (1009,10009,109,'2010-03-06 09:25');
INSERT INTO orders(order_id, order_code, encounter_id, created_dt) VALUES (1010,10010,110,'2010-03-22 11:18');

And here is the query that I tried:

SELECT
  u.user_id,
  name,
  ROW_NUMBER() OVER (
    PARTITION BY u.user_id ORDER BY o.created_dt ASC
  ) AS position,
  SUM (c.cost) OVER (
    PARTITION BY o.encounter_id
  ) AS cost,
  SUM (cost) OVER (
    PARTITION BY u.user_id
  ) AS sum
FROM
  users u
INNER JOIN
  encounter e USING (user_id)
INNER JOIN
  orders o USING (encounter_id)
INNER JOIN
  orders_catalog c USING (order_code)
ORDER BY name, position;

But the output is not what I expect: user_id|name|position|cost|sum -|-|-|-|- 2 |Charles |1 |214.11 |454.13 2 |Charles |2 |240.02 |454.13 3 |Eva |1 |214.11 |360.96002 3 |Eva |2 |146.85 |360.96002 5 |Helene |1 |168.18 |308.2 5 |Helene |2 |140.02 |308.2 4 |John |1 |181.03 |343.16 4 |John |2 |162.13 |343.16 1 |Peter |1 |100.34 |520.38 1 |Peter |2 |180.02 |520.38 1 |Peter |3 |240.02 |520.38 Since I would want something like: user_id|name|position|cost|sum -|-|-|-|- ...|...|...|...|... 1 |Peter |1 |100.34 |100.34 1 |Peter |2 |180.02 |280.36 1 |Peter |3 |240.02 |520.38 Fiddle