Upon submitting form, scroll to vertical position on page - php

Question

I have created a simple html/php form where visitors on my site can write their name, email and message and then send the message to my email. Problem is that when they submit the email, my site then performs a full refresh (it looks like) and therefore just reloads to the top of my site. I would like for the user to remain at the same scroll position after submit, so that they can instantly see whether the submit was succesful or not. So either a solution that prevents the refresh or some other solution that automatically scrolls down vertical to the form.
Can you tell me if this is possible using php? Or do I have to use some jquery/ajax solution?
Below is the code I am using. I am a complete novice, so please be gentle.
<form action="" method="post" id="form">
<div class="contact-info-group">
<label for="name"><span>Your name</span>
<input type="text" id="name" name="name" autocomplete="off" value="<?php echo $name; ?>"></label>
<label for="email"><span>Your email</span>
<input type="email" id="email" name="email" autocomplete="off"></label>
</div>
<label for="message"><span>Your message</span>
<textarea id="message" name="message"></textarea></label>
<input id="button1" type="submit" class="button next" name="contact_submit" value="Send message">
<?php
// Check for header injections
function has_header_injection($str) {
return preg_match("/[\r\n]/", $str);
}
if (isset ($_POST['contact_submit'])) {
$name = trim($_POST['name']);
$email = trim($_POST['email']);
$msg = $_POST['message'];
// Check to see if $name or $email have header injections
if (has_header_injection($name) || has_header_injection($email)) {
die();
}
if (!$name || !$email || !$msg) {
echo '<div class="contact-warning"><h2>! Error - Please note that all of the above fields are required !</h2></div>';
exit;
}
// Add the recipient email to a variable
$to = "email#email.com";
// Create a subject
$subject = "Message via website.com - $name";
// Construct the message
$message = "Name: $name\r\n";
$message .= "Email: $email\r\n";
$message .= "Message: \r\n\r\n$msg";
// Clean up the message
$message = wordwrap($message, 72);
// Set the mail headers into a variable
$headers = "MIME-Version 1.0\r\n";
$headers .= "Content-type: text/plain; charset=iso-8859-1\r\n";
$headers .= "From: $name <$email> \r\n";
$headers .= "X-Priority: 1\r\n";
$headers .= "X-MSMail-Priority: High\r\n\r\n";
// Send the email
mail($to, $subject, $message, $headers);
echo '<div class="contact-warning"><h2>Thank you for your message. We will get back to you shortly.</h2></div>';
}
?>
</form>