String url="https://miejemplo.com";

@Override
protected void onCreate(Bundle savedInstanceState) {
    super.onCreate(savedInstanceState);
    setContentView(R.layout.activity_main);

    WebView view = (WebView) findViewById(R.id.view);
    view.getSettings().setJavaScriptEnabled(true);
    view.setWebViewClient(new MyWebViewClient());
    view.loadUrl(url);
}


private class MyWebViewClient extends WebViewClient{

     public boolean shouldOverrideUrLoading(WebView view, String url){
        view.loadUrl(url);
         return true; //permite que la página se refresque en el webview
            }
}