Have the server return HTTP 204 (No Content) after the form submission. According to the HTTP 1.1 spec:
10.2.5 204 No Content
The server has fulfilled the request
but does not need to return an
entity-body, and might want to return
updated metainformation. The response
MAY include new or updated
metainformation in the form of
entity-headers, which if present
SHOULD be associated with the
requested variant.
If the client is a user agent, it
SHOULD NOT change its document view
from that which caused the request to
be sent. This response is primarily
intended to allow input for actions to
take place without causing a change to
the user agent's active document view,
although any new or updated
metainformation SHOULD be applied to
the document currently in the user
agent's active view.
The 204 response MUST NOT include a
message-body, and thus is always
terminated by the first empty line
after the header fields.
This sounds like exactly what you want.