Form submission not working - php

Question

I have a problem with the Form I'm trying to create. Basically, it does not allow me to send the email to the recipient, even though the PHP code is correct. Few people from SO already tried to help, but it seems the code is not working.
<?php
$error = false;
$sent = false;
if(isset($_POST['submit'])) {
if(empty($_POST['name']) || empty($_POST['email']) || empty($_POST['comments'])) {
$error = true;
}
else {
$to = "linardsberzins#gmail.com";
$name = trim($_POST['name']);
$email = trim($_POST['email']);
$comments = trim($_POST['comments']);
$subject = "Contact Form";
$message = "Name: $name \r\n Email: $email \r\n Comments: $comments";
$headers = "From:" . $name;
$mailsent = mail($to, $subject, $message, $headers);
if($mailsent) {
$sent = true;
}
}
}
?>
HTML:
<?php if($error == true){ ?>
<p class="error">Text</p>
<?php } if($sent == true) { ?>
<p class="sent">Text</p>
<?php } ?>
<div id="form">
<form name="contact" action="<?php echo $_SERVER['PHP_SELF']; ?>" method="post">
<fieldset>
<h4>Contact Me!</h4>
<label for="name">Name:</label>
<input type="text" name="name" id="name"/>
<label for="email"/>Email:</label>
<input type="text" name="email" id="email"/>
<label for="comments" id="comments">Comments:</label>
<textarea name="comments" id=""></textarea>
<fieldset>
<input class="btn" type="submit" name="submit" class="submit" value="Send email"/>
<input class="btn" type="reset" value="Reset"/>
</fieldset>
</fieldset>
</form>

Answer 1

Do not rely on submit button as not all browsers send that button as a POST, change to other input:
if(isset($_POST['name'])) {