Your button has a class name,you can find your button using class name,see this example:
private void Form1_Load(object sender, EventArgs e)
{
webBrowser1.DocumentText = "<td class=\"submit\"><br><button class=\"fixedSizeBigButton\" type=\"submit\"></td>";
webBrowser1.DocumentCompleted += new WebBrowserDocumentCompletedEventHandler(webBrowser1_DocumentCompleted);
}
void webBrowser1_DocumentCompleted(object sender, WebBrowserDocumentCompletedEventArgs e)
{
foreach (HtmlElement btn in webBrowser1.Document.GetElementsByTagName("button"))
{
if (btn.GetAttribute("ClassName") == "fixedSizeBigButton")
{
btn.InvokeMember("Click");
}
}
}