How to store text content of a browser textarea on a local disk

I need to store edited "textarea" text ( > 1 MB ) temporarily on a local disk to work offline. Later I want to load it again and continue editing, just like a with common desktop apps. I know I can load textfiles easily and add it to an textarea. But how to save it ? I'v red a lot in blogs about this issue and there are some serious workaround proposals like IndexdDB and Web SQL Storage. But which one is working on all major browsers and will be supported in the (near) future ? I did not find any current clear statement yet.