fix(poly): coefficients properly handle chain rule

src/poly/coeff/private/polyCoeff.cpp

@@ -2,7 +2,7 @@
 //
 //   Copyright (C) 2025 -- The 4D-STAR Collaboration
 //   File Author: Emily Boudreaux
-//   Last Modified: February 14, 2025
+//   Last Modified: March 18, 2025
 //
 //   4DSSE is free software; you can use it and/or modify
 //   it under the terms and restrictions the GNU General Library Public
@@ -19,21 +19,23 @@
 //
 // *********************************************************************** */
 #include "mfem.hpp"
-#include <iostream>
 
 #include "polyCoeff.h"
 
 namespace polycoeff{
   double nonlinearSourceCoeff(const mfem::Vector &x)
   {
-    // double r = x.Norml2();
-    return 1.0;
+    double r = x.Norml2();
+    return std::pow(r, 2);
   }
 
   void diffusionCoeff(const mfem::Vector &x, mfem::Vector &v)
   {
     v.SetSize(3);
-    for (int i = 0; i < 3; i++) { v(i) = -1; }
+    double r = x.Norml2();
+    for (int i = 0; i < 3; i++) { 
+      v(i) = -std::pow(r, 2);
+    }
   }
 
   double x1(const double n)