data_d2.dat

dof        l2_err     level
5          8.312e-02  2
17         2.547e-02  3
49         7.407e-03  4
129        2.102e-03  5
321        5.874e-04  6
769        1.623e-04  7
1793       4.442e-05  8
4097       1.207e-05  9
9217       3.261e-06  10

data_d3.dat

dof        l2_err     level
7          8.472e-02  2
31         3.044e-02  3
111        1.022e-02  4
351        3.303e-03  5
1023       1.039e-03  6
2815       3.196e-04  7
7423       9.658e-05  8
18943      2.873e-05  9
47103      8.437e-06  10

data_d4.dat

dof        l2_err     level
9          7.881e-02  2
49         3.243e-02  3
209        1.232e-02  4
769        4.454e-03  5
2561       1.551e-03  6
7937       5.236e-04  7
23297      1.723e-04  8
65537      5.545e-05  9
178177     1.751e-05  10

pgf.tex

\documentclass{article}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=1.9}

% See `texdoc pgfplots` and `texdoc pgfplotstable` for more information.

\begin{document}
\begin{tikzpicture}
  \begin{axis}[
    axis lines=center,
    samples=40,
    xlabel={$x$},
    ylabel={$x^2$},
    domain=-5:5,
    ytick={0,4,...,24},
    xtick={-5,-4,...,5},
    grid=major,
    ]
    \addplot+[no marks] {x^2};
  \end{axis}
\end{tikzpicture}

\begin{tikzpicture}
  \begin{loglogaxis}[
    title=Convergence Plot,
    xlabel=Degrees of Freedom,
    ylabel=$L_2$ Error,
    legend entries={$d=2$,$d=3$,$d=4$},
    ]
    \addplot table {data_d2.dat};
    \addplot table {data_d3.dat};
    \addplot table {data_d4.dat};
  \end{loglogaxis}
\end{tikzpicture}
\end{document}