Though you have used 'button' type instead of 'input' but when browser render your web page it automatically converts it to 'input', check below snippet and see if it works for you
HtmlElementCollection elc = this.webBrowser1.Document.GetElementsByTagName("input");
foreach (HtmlElement el in elc)
{
if (el.GetAttribute("type").Equals("submit"))
{
el.InvokeMember("Click");
}
}
above code collect a tag from HTML source start with 'input' and then check of the type of the tag is submit, if it is. then it will directly Invoke click method.
OR
Other way is to check the view source and copy the 'id' of your web button and used it in below code
private void webBrowser1_DocumentCompleted(object sender, WebBrowserDocumentCompletedEventArgs e)
{
webBrowser1.Document
.GetElementById("HTMLID_of_your_web_button")
.InvokeMember("Click");
}