Best way to refresh a client browser after they initiated a MySQL insert/update?

For example, say a user has a web page displayed on their local computer. They also have another page with a form (on the same domain) open on their smartphone. They submit the form which inserts or updates a MySQL database. I'd then want the browser on their local computer to immediately reflect the change they just submitted.

What's the best way to accomplish this?

I was thinking of triggering a page reload after the table was updated but not sure if that's doable/efficient.