stiff_1d_sp

 STIFF_1D_SP    Computes local stiffness matrix for 1D problem

     [A]=stiff_1d_sp(w,d,jac) computes stiffness matrix A:
         A_{ij} = ( (phi_j)',(phi_i)')_N
         by Galerkin-Numerical Integration

 Input: 
        w = npdx LGL weigths in [-1,1],  
            (produced by calling [x,w]=xwlgl(npdx))
            (npdx = number of nodes, =n+1, if n=polynomial degree)
        d = first derivative LGL matrix (produced by calling d=derlgl(x,npdx))
        jac =  jacobian of the map F:[-1,1]---->[a,b]

 Output: A = matrix (npdx,npdx) with the stiffness contribution

 Reference: CHQZ2 = C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang,
                    "Spectral Methods. Fundamentals in Single Domains"
                    Springer Verlag, Berlin Heidelberg New York, 2006.

0001 function [A]=stiff_1d_sp(w,d,jac)
0002 % STIFF_1D_SP    Computes local stiffness matrix for 1D problem
0003 %
0004 %     [A]=stiff_1d_sp(w,d,jac) computes stiffness matrix A:
0005 %         A_{ij} = ( (phi_j)',(phi_i)')_N
0006 %         by Galerkin-Numerical Integration
0007 %
0008 % Input:
0009 %        w = npdx LGL weigths in [-1,1],
0010 %            (produced by calling [x,w]=xwlgl(npdx))
0011 %            (npdx = number of nodes, =n+1, if n=polynomial degree)
0012 %        d = first derivative LGL matrix (produced by calling d=derlgl(x,npdx))
0013 %        jac =  jacobian of the map F:[-1,1]---->[a,b]
0014 %
0015 % Output: A = matrix (npdx,npdx) with the stiffness contribution
0016 %
0017 % Reference: CHQZ2 = C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang,
0018 %                    "Spectral Methods. Fundamentals in Single Domains"
0019 %                    Springer Verlag, Berlin Heidelberg New York, 2006.
0020 
0021 %   Written by Paola Gervasio
0022 %   $Date: 2007/04/01$
0023 
0024 A=d'*diag(w)*d;
0025 A=A/jac;
0026 return