What happens to your savings will depend on your situation. Are you living together? Are you married?

You own the money in your own savings account, by which we mean any savings account that is held only in your name. If you separate from your partner, those savings will therefore remain your property.

However, your partner may have power of attorney over your savings account, meaning that your partner can access your savings. This power of attorney can be withdrawn at any time without your partner's permission.

If you have a joint account with your partner, that means you have given each other power of attorney to manage the account. You and your partner can both access the savings in the account as long as that power of attorney is active. You or your partner may revoke the power of attorney when you separate, That means that neither of you are able to access the savings account independently anymore. You will both have to be present in order to access the savings.

The savings in your joint account must be split between you. If you are de facto or de jure cohabitants, you will remain the owner of your own sources of income, such as your salary. If you want to split the savings, you must first demonstrate what money belongs to you.

You are required to notify your bank if you decide to divorce. 

If you are married without a pre-nuptial agreement, then in the eyes of the law you are married 'in community of property'. That means that all of your income is shared. The money in your own savings account can also belong to your partner from a legal point of view.

A joint savings account belongs to both partners. You may act separately from each other,  and both you and your partner can access the money in the account. When you separate from your partner, both you and your partner may block the account. That means that neither of you are able to access the savings account independently anymore.

Of course, you can reach your own agreement on how to split the money in the joint savings account (mutual consent). If your divorce goes to court, the judge will divide the money.

If you have a pre-nuptial agreement, you can be married with 'separation of property'. An agreement of this kind specifies which assets and sources of income belong to you and which to your partner. You should therefore refer to the pre-nuptial agreement in order to find out who the savings belong to and how they should be split. After all, a pre-nuptial agreement can also be a variant of the legal system, meaning that you can still be married 'in community of property'.