Post Form Results to Table in Same page

You can have an ajax action that sent the data to the backend populate the table and return the success or the errors back.

You can use this actions

add_action('wp_ajax_*', 'custom_table_insert');
add_action('wp_ajax_nopriv_*', 'custom_table_insert'); // anonymous users

This will give you more control and ultimately a far better user experience.
// Ajax Request template

jQuery.ajax({
        url : your_settings_object.ajax_url,
        type : 'post',
        data : {
            action : 'wp_ajax_*',
            table_content : table_content
        },
        success : function( response ) {
            alert(response)
        }
    });

Note: your_settings_object is a custom object that use to transfer global variables from backend to JS
Also the table_content is your variable to pass the data and you can take them from the PHP with $_POST['table_content']