Uniformisation of the weights of the Gauss Quadrature points (sum = volume of the reference element)
Adding Gauss Quadrature rule for a line
Modifications by Gaetan Bricteux

Numeric/Gauss.h

-// Gmsh - Copyright (C) 1997-2009 C. Geuzaine, J.-F. Remacle
+// Gmsh - Copyright (C) 1997-2008 C. Geuzaine, J.-F. Remacle
 //
 // See the LICENSE.txt file for license information. Please report all
 // bugs and problems to <gmsh@geuz.org>.
@@ -15,6 +15,9 @@ int GaussLegendreTri(int n1, int n2, IntPt *pts);
 int GaussLegendreTet(int n1, int n2, int n3, IntPt *pts); 
 int GaussLegendreHex(int n1, int n2, int n3, IntPt *pts);
 
+int getNGQLPts (int order);
+IntPt *getGQLPts (int order);
+
 int getNGQTPts(int order);
 IntPt *getGQTPts (int order);
 

Numeric/GaussLegendre1D.h

-// Gmsh - Copyright (C) 1997-2009 C. Geuzaine, J.-F. Remacle
+// Gmsh - Copyright (C) 1997-2008 C. Geuzaine, J.-F. Remacle
 //
 // See the LICENSE.txt file for license information. Please report all
 // bugs and problems to <gmsh@geuz.org>.
 
-#ifndef _GAUSS_LEGENDRE_1D_H_
-#define _GAUSS_LEGENDRE_1D_H_
-
 /* 1 point rule points */
 static double _GL_pt1[1]={
   0.000000000000000e+00};
@@ -124,7 +121,8 @@ static double _GL_wt6[6]={
  /* 15 point rule weights */
  static double _GL_wt15[15]={
   3.075324199611663e-02, 7.036604748810814e-02, 1.071592204671720e-01, 1.395706779261543e-01, 1.662692058169940e-01, 1.861610000155622e-01, 1.984314853271116e-01, 2.025782419255613e-01, 1.984314853271116e-01, 1.861610000155622e-01, 1.662692058169940e-01, 1.395706779261543e-01, 1.071592204671720e-01, 7.036604748810814e-02, 3.075324199611663e-02};
-/* 16 point rule points */
+
+ /* 16 point rule points */
  static double _GL_pt16[16]={
  -9.894009349916499e-01,-9.445750230732326e-01,-8.656312023878318e-01,-7.554044083550030e-01,-6.178762444026438e-01,-4.580167776572274e-01,-2.816035507792589e-01,-9.501250983763744e-02, 9.501250983763744e-02, 2.816035507792589e-01, 4.580167776572274e-01, 6.178762444026438e-01, 7.554044083550030e-01, 8.656312023878318e-01, 9.445750230732326e-01, 9.894009349916499e-01};
 
@@ -132,6 +130,14 @@ static double _GL_wt6[6]={
  static double _GL_wt16[16]={
   2.715245941175406e-02, 6.225352393864778e-02, 9.515851168249290e-02, 1.246289712555339e-01, 1.495959888165768e-01, 1.691565193950026e-01, 1.826034150449236e-01, 1.894506104550685e-01, 1.894506104550685e-01, 1.826034150449236e-01, 1.691565193950026e-01, 1.495959888165768e-01, 1.246289712555339e-01, 9.515851168249290e-02, 6.225352393864778e-02, 2.715245941175406e-02};
 
+ /* 20 point rule points */
+ static double _GL_pt20[20]={
+ -9.931285991850949e-01, -9.639719272779138e-01, -9.122344282513259e-01, -8.391169718222188e-01, -7.463319064601508e-01, -6.360536807265150e-01, -5.108670019508271e-01, -3.737060887154196e-01, -2.277858511416451e-01, -7.652652113349733e-02, 7.652652113349733e-02, 2.277858511416451e-01, 3.737060887154196e-01, 5.108670019508271e-01, 6.360536807265150e-01, 7.463319064601508e-01, 8.391169718222188e-01, 9.122344282513259e-01, 9.639719272779138e-01, 9.931285991850949e-01};
+
+ /* 20 point rule weights */
+ static double _GL_wt20[20]={
+  1.761400713915212e-02, 4.060142980038694e-02, 6.267204833410906e-02, 8.327674157670475e-02, 1.019301198172404e-01, 1.181945319615184e-01, 1.316886384491766e-01, 1.420961093183821e-01, 1.491729864726037e-01, 1.527533871307259e-01, 1.527533871307259e-01, 1.491729864726037e-01, 1.420961093183821e-01, 1.316886384491766e-01, 1.181945319615184e-01, 1.019301198172404e-01, 8.327674157670475e-02, 6.267204833410906e-02, 4.060142980038694e-02, 1.761400713915212e-02};
+
 inline void gmshGaussLegendre1D(int nbQuadPoints, double **t, double **w)
 {
   switch (nbQuadPoints){
@@ -199,6 +205,10 @@ inline void gmshGaussLegendre1D(int nbQuadPoints, double **t, double **w)
     *t = _GL_pt16;
     *w = _GL_wt16;
     break;
+  case 20:
+    *t = _GL_pt20;
+    *w = _GL_wt20;
+    break;
   default :
     *t = 0;
     *w = 0;
@@ -206,4 +216,3 @@ inline void gmshGaussLegendre1D(int nbQuadPoints, double **t, double **w)
   }
 }
 
-#endif

Numeric/GaussLegendreSimplex.cpp

-// Gmsh - Copyright (C) 1997-2009 C. Geuzaine, J.-F. Remacle
+// Gmsh - Copyright (C) 1997-2008 C. Geuzaine, J.-F. Remacle
 //
 // See the LICENSE.txt file for license information. Please report all
 // bugs and problems to <gmsh@geuz.org>.
@@ -47,7 +47,7 @@ int GaussLegendreTet(int n1, int n2, int n3, IntPt *pts)
       for(k=0; k < n3; k++) {
         brickToTet(pt1[i],pt2[j],pt3[k],&(pts[index].pt[0]),
                    &(pts[index].pt[1]),&(pts[index].pt[2]),&dJ);
-	pts[index++].weight = dJ*wt1[i]*wt2[j]*wt3[k]*6.0;
+	pts[index++].weight = dJ*wt1[i]*wt2[j]*wt3[k];
       }
     }
   }
@@ -67,7 +67,7 @@ int GaussLegendreTri(int n1,int n2,IntPt *pts)
     for(j=0; j < n2; j++) {
       quadToTri(pt1[i],pt2[j],&(pts[index].pt[0]),&(pts[index].pt[1]),&dJ);
       pts[index].pt[2] = 0;
-      pts[index++].weight = dJ*wt1[i]*wt2[j]*2.0;
+      pts[index++].weight = dJ*wt1[i]*wt2[j];
     }
   }
   return index;

Numeric/GaussQuadratureHex.cpp

-// Gmsh - Copyright (C) 1997-2009 C. Geuzaine, J.-F. Remacle
+// Gmsh - Copyright (C) 1997-2008 C. Geuzaine, J.-F. Remacle
 //
 // See the LICENSE.txt file for license information. Please report all
 // bugs and problems to <gmsh@geuz.org>.
@@ -61,7 +61,7 @@ IntPt *getGQHPts(int order);
 int getNGQHPts(int order);
 
 IntPt * GQH[17] = {GQH1,GQH1,GQH6,GQH8,0,0,0,0,0,0,0,0,0,0,0,0,0};
-int GQHnPt[4] = {1,4,5,15};
+int GQHnPt[4] = {1,1,6,8};
 
 IntPt *getGQHPts(int order)
 { 

Numeric/GaussQuadratureLin.cpp

+// Gmsh - Copyright (C) 1997-2008 C. Geuzaine, J.-F. Remacle
+//
+// See the LICENSE.txt file for license information. Please report all
+// bugs and problems to <gmsh@geuz.org>.
+
+#include "Gauss.h"
+#include "GaussLegendre1D.h"
+
+IntPt * GQL[20] = {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0};
+
+IntPt *getGQLPts(int order)
+{ 
+  int n = (order+1)/2;
+  int index = n;
+  if(!GQL[index]) {
+    double *pt,*wt;
+    gmshGaussLegendre1D(n,&pt,&wt);
+    GQL[index] = new IntPt[n];
+    for(int i=0; i < n; i++) {
+      GQL[index][i].pt[0] = pt[i];
+      GQL[index][i].pt[1] = 0.0;
+      GQL[index][i].pt[2] = 0.0;
+      GQL[index][i].weight = wt[i];
+    }
+  }
+  return GQL[index];
+}
+
+int getNGQLPts(int order)
+{ 
+  return (order+1)/2;
+}

Numeric/GaussQuadratureQuad.cpp

-// Gmsh - Copyright (C) 1997-2009 C. Geuzaine, J.-F. Remacle
+// Gmsh - Copyright (C) 1997-2008 C. Geuzaine, J.-F. Remacle
 //
 // See the LICENSE.txt file for license information. Please report all
 // bugs and problems to <gmsh@geuz.org>.
@@ -7,7 +7,7 @@
 #include "GaussLegendre1D.h"
 
 IntPt GQQ1[1] = {
-  { {0.0,0.0},4.0 }
+  { {0.0,0.0,0.0},4.0 }
 };
 
 const double xq3[3] = {0.816496580928,-0.408248290464,-0.408248290464};
@@ -108,7 +108,7 @@ int GQQnPt[7] = {1,1,3,4,7,9,16};
 IntPt *getGQQPts(int order)
 { 
   
-  if(order<1)return GQQ[order];
+  if(order<2)return GQQ[order];
   if(order==2)return GQQ[3];
   if(order==3)return GQQ[3];
 
@@ -138,7 +138,7 @@ int getNGQQPts(int order)
   if(order == 3)return 4;
   if(order == 2)return 4;
 
-  if(order < 1)
+  if(order < 2)
     return GQQnPt[order]; 
   return ((order+3)/2)*((order+3)/2);
 }