I understand that if I feel satisfied with an answer, I can (and should) accept it.
But should I upvote the accepted (or other) answers to my own question as well?
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It's really up to you. I'd only not upvote an answer that I accepted if I were out of votes for the day. Even then, I'd circle back and upvote it the next day. If it was helpful enough that it solved my problem, I certainly think it's deserving of an additional upvote.
For other (not accepted) answers it's not as certain, but if someone added to my understanding of a problem I was having, I'll give them an upvote.
The bottom line, though, is that how you spend your votes is totally up to you. You aren't forced to vote at all, but it is the most immediate way to give feedback, so it is encouraged.
Accepting and voting are separate and mean different things.
Accepting an answer means "this answer solved my problem". Don't feel pressure to accept an answer just because someone asked you too, unless you feel it actually did solve your problem.
Upvoting means this answer was helpful. Something can be helpful without solving your problem and likewise, it could have solved your problem (or answered your question) without being very helpful. Obviously if it solved your problem, it was at least somewhat helpful, but there are answers that you get that just don't offer much more than a couple of lines of code with no explanation or a one-word or one-sentence answer and in those cases you could chose not to upvote simply because the OP was not being very helpful. Again, that is based on your personal voting criteria, but this is how I would tend to evaluate it.
You should always upvote an answer that you found helpful. How you define helpful is up to you, but I generally upvote answers that provide a good solution to the problem (that works) or taught me something I didn't know, or pointed out a flaw in my design or logic.
So you have three choices when it comes to upvoting and accepting:
My rule of thumb is to accept the answer that best answered your question, and upvote the answers that are helpful and informative. (The two may not be the same.) Upvote exactly as you would if you were just browsing another question.
You can think about it this way: "Should the identity of the question asker influence whether I up-vote answers to that question?". Of course not.
You up-vote an answer based on its merit. Why should you act differently when it comes to your question?