I've been testing extrapolate for interpolation purposes and noticed what appears to be a bug (code below). When extrapolating more than one order higher in interpolation levels (say Lagrange order 1 to Lagrange order 3) oscillations appear in the extrapolated higher order function. The following is a test code which generates data for y=x^5 at non-regular intervals, x_i = i*(1+*0.1), and tests extrapolating the data to higher basis functions at x=3. The following is the output: 3^5 : 243 <--- expected O(1): 298.676 O(2): 228 O(3): 234.062 O(4): 88.9269 Note that the values start to diverge. The errors behave differently with different data and testing points, but this demonstrates the problem. The UFL files look like: element = FiniteElement("Lagrange", interval, 1) # Interpolate1.ufl element = FiniteElement("Lagrange", interval, 2) # Interpolate2.ufl element = FiniteElement("Lagrange", interval, 3) # Interpolate3.ufl element = FiniteElement("Lagrange", interval, 4) # Interpolate4.ufl Here's the code: // Setup data vectors int n = 9; // Setup data vectors boost::shared_ptr xs(new Vector(n)); boost::shared_ptr ys(new Vector(n)); // Populate test data for(int i=0; isetitem(i,i+i*0.1); ys->setitem(i,(*xs)[i]*(*xs)[i]*(*xs)[i]*(*xs)[i]*(*xs)[i]); } // Setup the mesh to interpolate on // Note the count is the number of elements, not nodes boost::shared_ptr mesh (new Interval(n-1,0,1)); for(int i=0; icoordinates()[i] = (*xs)[i]; // create the function space of order one. // this is done so that dof maps directly to // data points. boost::shared_ptr V (new Interpolate1::FunctionSpace(mesh)); // copy the data into the function space Function fy (V, ys); boost::shared_ptr V2 (new Interpolate2::FunctionSpace(mesh));; boost::shared_ptr V3 (new Interpolate3::FunctionSpace(mesh));; boost::shared_ptr V4 (new Interpolate4::FunctionSpace(mesh));; Function fy2 (V2); Function fy3 (V3); Function fy4 (V4); fy2.extrapolate(fy); fy3.extrapolate(fy); fy4.extrapolate(fy); std::cout << "3^5 : " << 3*3*3*3*3 << "\n" << "O(1): " << fy(3) << "\tO(2): " << fy2(3) << "\tO(3): " << fy3(3) << "\tO(4): " << fy4(3) << "\n"; Thoughts?

When	Who	Action	New State
2011-11-30	Charles Cook	Comment	Open
2011-11-30	Charles Cook	Comment	Open
2011-11-30	Anders Logg	Answer	Answered
2011-11-30	Charles Cook	Reopen	Open
2011-12-16	Launchpad Janitor	Expire	Expired

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