[examples] Add skeleton for nested iteration to adaptive example

examples/poisson-adaptive.cc

@@ -262,6 +262,9 @@ int main (int argc, char *argv[]) try
 
   // Discretize -> solve -> estimate -> mark -> refine
 
+  using Vector = Dune::BlockVector<double>;
+  auto sol_initial = Vector();
+
   std::size_t refinementStep = 0;
   while(true)
   {
@@ -344,8 +347,13 @@ int main (int argc, char *argv[]) try
     // Initialize solution vector
     // *********************************************
 
-    Dune::Functions::istlVectorBackend(sol).resize(basis);
-    Dune::Functions::istlVectorBackend(sol) = 0;
+    // For simplicity use zero as initial value.
+    // Here we could use an adapted solution from
+    // the previous grid as initial value.
+    Dune::Functions::istlVectorBackend(sol_initial).resize(basis);
+    Dune::Functions::istlVectorBackend(sol_initial) = 0;
+
+    sol = sol_initial;
 
     // *********************************************
     // Solve linear system
@@ -441,6 +449,7 @@ int main (int argc, char *argv[]) try
       // *********************************************
 
       {
+        auto u_initial = bindToCoefficients(trialFunction(basis), sol_initial);
         auto d = bindToCoefficients(trialFunction(extensionBasis), defect);
 #if DUNE_VERSION_GT(DUNE_VTK, 2, 9)
         using Dune::Vtk::LagrangeDataCollector;
@@ -448,6 +457,7 @@ int main (int argc, char *argv[]) try
         using Dune::VTK::FieldInfo;
         auto vtkWriter = UnstructuredGridWriter(LagrangeDataCollector(basis.gridView(), extensionOrder));
         vtkWriter.addPointData(u, FieldInfo("sol", FieldInfo::Type::scalar, 1));
+        vtkWriter.addPointData(u_initial, FieldInfo("sol_initial", FieldInfo::Type::scalar, 1));
         vtkWriter.addPointData(d, FieldInfo("defect", FieldInfo::Type::scalar, 1));
         vtkWriter.write(Dune::formatString("poisson-adaptive-%03d", refinementStep));
 #else