# L-zwei-Fehlernormen gem Definition (7.133) fr die Residuen aus Bild
# 7.4:
# 
> L_2:=sqrt(int(R(xi)^2,xi=0..1));

                            /   1           \1/2
                            |  /            |
                            | |        2    |
                     L_2 := | |   R(xi)  dxi|
                            | |             |
                            |/              |
                            \  0            /

# Fr die einzelnen Residuen aus Bild 7.4 erhlt man folgen
# L-zwei-Fehlernormen:
# 
> R[1](xi):=-(1/2)*(1-5*xi^2);

                                              2
                                          5 xi
                      R[1](xi) := - 1/2 + -----
                                            2

> L_2[1]:=sqrt(Int(R[1]^2,xi=0..1))=sqrt(int(R[1](xi)^2,xi=0..1));

                           /   1          \1/2
                           |  /           |       1/2
                           | |       2    |      6
                 L_2[1] := | |   R[1]  dxi|    = ----
                           | |            |       3
                           |/             |
                           \  0           /

> L_2[1]:=evalf(sqrt(6)/3);

                        L_2[1] := 0.8164965809

> R[2](xi):=2-(1-xi^2)*(2.44-2.02*xi^2+12.12*xi^4);

                              2                 2           4
       R[2](xi) := 2 - (1 - xi ) (2.44 - 2.02 xi  + 12.12 xi )

> L_2[2]:=sqrt(Int(R[2]^2,xi=0..1))=sqrt(int(R[2](xi)^2,xi=0..1));

                       /   1          \1/2
                       |  /           |
                       | |       2    |
             L_2[2] := | |   R[2]  dxi|    = 0.4220959810
                       | |            |
                       |/             |
                       \  0           /

> R[3](xi):=2-(1-xi^2)*(2.44-2.17*xi^2+13.01*xi^4+2.95*xi^6-7.37*xi^8);

  R[3](xi) := 2 -

               2                 2           4          6          8
        (1 - xi ) (2.44 - 2.17 xi  + 13.01 xi  + 2.95 xi  - 7.37 xi )

> L_2[3]:=sqrt(Int(R[3]^2,xi=0..1))=sqrt(int(R[3](xi)^2,xi=0..1));

                       /   1          \1/2
                       |  /           |
                       | |       2    |
             L_2[3] := | |   R[3]  dxi|    = 0.4666252637
                       | |            |
                       |/             |
                       \  0           /

