Spacing of rows in a table

Question

I am using package tabular but encounter a problem with the spacing of rows, I would like to have more space at the top and at the bottom of each formula. I already looked at older posts dealing with this issue and they suggested to use arraystretch but it stretches all the rows (I don't want first row to be stretched for example) but most importantly unequally (there is more space at the top than at the bottom).

This is what my table currently looks like:

This is what arraystretch (with factor 3) do to it:

In both cases it is not aesthetically pleasing. And I can't seem to find any simple solution to my problem.

Here's my code:

\documentclass{article}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage[french]{babel}
\usepackage{array}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{lmodern}
\begin{document}
\begin{center}
\begin{tabular}{|c|c|c|}
\hline 
Nom de la méthode & Formule de majoration de l'erreur & Ordre de convergence \ 
\hline 
Rectangles à gauche & $|E_h^{RG}(f)| \leq \dfrac{h}{2} (\beta-\alpha)\lVert f'\rVert_{\infty}^{[a,b]}$ & 1 \ 
\hline
Point Milieu &  $|E_h^{PM}(f)| \leq \dfrac{h^2}{24} (\beta-\alpha)\lVert f^{(2)}\rVert_{\infty}^{[a,b]}$ & 2 \ 
\hline 
Trapèzes & $|E_h^T(f)| \leq \dfrac{h^2}{12} (\beta-\alpha)\lVert f^{(2)}\rVert_{\infty}^{[a,b]}$ & 2 \ 
\hline 
Simpson & $|E_h^S(f)| \leq \dfrac{h^4}{2880} (\beta-\alpha)\lVert f^{(4)}\rVert_{\infty}^{[a,b]}$ & 4 \ 
\hline 
\end{tabular} 
\end{center}
\end{document}

Answer 1

The most elegant typographic approach to keep stuff from getting too close to horizontal lines in a table? Easy: Don't use horizontal lines!

Here's a tabularx-based implementation of this idea.

\documentclass{article}
\usepackage[french]{babel}
\usepackage[T1]{fontenc}
%\usepackage[utf8]{inputenc} % that's the default nowadays
\usepackage{lmodern}
\usepackage{amssymb,mathtools}
\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}
\DeclarePairedDelimiter{\norm}{\lVert}{\rVert}
\usepackage{tabularx,booktabs,ragged2e}
\newcolumntype{C}{>{\Centering}X} $ centered version of 'X' col. type
\newcolumntype{L}{>{$\displaystyle}l<{$}} % automatic math mode
\begin{document}
\noindent
\begin{tabularx}{\textwidth}{@{} l >{$\displaystyle}l<{$} C @{}}
\toprule
Nom de la méthode & $Formule de majoration de l'erreur$ & Ordre de convergence \ 
\midrule 
Rectangles à gauche & 
   \abs{E_h^{\mathit{RG}}(f)} \le \frac{h}{2}    (\beta-\alpha) \norm[\big]{f'}{\infty}^{[a,b]}      & 1 \ 
\addlinespace
Point Milieu &

   \abs{E_h^{\mathit{PM}}(f)} \le \frac{h^2}{24} (\beta-\alpha) \norm[\big]{f^{(2)}}{\infty}^{[a,b]} & 2 \ 
\addlinespace 
Trapèzes & 
   \abs{E_h^T(f)} \le \frac{h^2}{12}   (\beta-\alpha) \norm[\big]{f^{(2)}} _{\infty}^{[a,b]}          & 2 \ 
\addlinespace 
Simpson & 
   \abs{E_h^S(f)} \le \frac{h^4}{2880} (\beta-\alpha) \norm[\big]{f^{(4)}} _{\infty}^{[a,b]}          & 4 \ 
\bottomrule 
\end{tabularx}
\end{document}

Answer 2

Here are three possibilities using makecell, nicematrix or tabularray:

\documentclass{article}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage[french]{babel}
\usepackage{array}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{lmodern}
%%% first example %%%
\usepackage{makecell}
\setcellgapes{4pt}
%%% second example %%%
\usepackage{nicematrix}
%%% third example %%%
\usepackage{tabularray}
\begin{document}
\begin{center}
\makegapedcells
\begin{tabular}{|c|c|c|}
\hline 
Nom de la méthode & Formule de majoration de l'erreur & Ordre de convergence \ 
\hline 
Rectangles à gauche & $|E_h^{RG}(f)| \leq \dfrac{h}{2} (\beta-\alpha)\lVert f'\rVert_{\infty}^{[a,b]}$ & 1 \ 
\hline
Point Milieu &  $|E_h^{PM}(f)| \leq \dfrac{h^2}{24} (\beta-\alpha)\lVert f^{(2)}\rVert_{\infty}^{[a,b]}$ & 2 \ 
\hline 
Trapèzes & $|E_h^T(f)| \leq \dfrac{h^2}{12} (\beta-\alpha)\lVert f^{(2)}\rVert_{\infty}^{[a,b]}$ & 2 \ 
\hline 
Simpson & $|E_h^S(f)| \leq \dfrac{h^4}{2880} (\beta-\alpha)\lVert f^{(4)}\rVert_{\infty}^{[a,b]}$ & 4 \ 
\hline 
\end{tabular} 
\end{center}
\begin{center}
\begin{NiceTabular}[hvlines, cell-space-limits=4pt]{ccc}
Nom de la méthode & Formule de majoration de l'erreur & Ordre de convergence \ 
Rectangles à gauche & $|E_h^{RG}(f)| \leq \dfrac{h}{2} (\beta-\alpha)\lVert f'\rVert_{\infty}^{[a,b]}$ & 1 \ 
Point Milieu &  $|E_h^{PM}(f)| \leq \dfrac{h^2}{24} (\beta-\alpha)\lVert f^{(2)}\rVert_{\infty}^{[a,b]}$ & 2 \ 
Trapèzes & $|E_h^T(f)| \leq \dfrac{h^2}{12} (\beta-\alpha)\lVert f^{(2)}\rVert_{\infty}^{[a,b]}$ & 2 \ 
Simpson & $|E_h^S(f)| \leq \dfrac{h^4}{2880} (\beta-\alpha)\lVert f^{(4)}\rVert_{\infty}^{[a,b]}$ & 4 \

\end{NiceTabular} 
\end{center}
\begin{center}
\SetTblrInner{rowsep=4pt}
\begin{tblr}{colspec={ccc}, hlines, vlines}
Nom de la méthode & Formule de majoration de l'erreur & Ordre de convergence \ 
Rectangles à gauche & $|E_h^{RG}(f)| \leq \dfrac{h}{2} (\beta-\alpha)\lVert f'\rVert_{\infty}^{[a,b]}$ & 1 \ 
Point Milieu &  $|E_h^{PM}(f)| \leq \dfrac{h^2}{24} (\beta-\alpha)\lVert f^{(2)}\rVert_{\infty}^{[a,b]}$ & 2 \ 
Trapèzes & $|E_h^T(f)| \leq \dfrac{h^2}{12} (\beta-\alpha)\lVert f^{(2)}\rVert_{\infty}^{[a,b]}$ & 2 \ 
Simpson & $|E_h^S(f)| \leq \dfrac{h^4}{2880} (\beta-\alpha)\lVert f^{(4)}\rVert_{\infty}^{[a,b]}$ & 4 \

\end{tblr} 
\end{center}
\end{document}

Answer 3

The tool for that is cellspace, which defines a minimal vertical spacing at the top and bottom of cells in columns with specifier prefixed with the letterS (or C if you load siunitx, or any letter you please with loadtime option [column=…]

\documentclass[a4paper]{book}
\usepackage{amsmath}
\usepackage{geometry} 
\usepackage{cellspace} 
\setlength{\cellspacetoplimit}{6pt}
\setlength{\cellspacebottomlimit}{6pt}
\begin{document}
\begin{table}[htb]
\centering
\begin{tabular}{|Sc|Sc|Sc|}
\hline
Nom de la méthode & Formule de majoration de l'erreur & Ordre de convergence \
\hline
Rectangles à gauche & $|E_h^{RG}(f)| \leq \dfrac{h}{2} (\beta-\alpha)\lVert f'\rVert_{\infty}^{[a,b]}$ & 1 \
\hline
Point Milieu & $|E_h^{PM}(f)| \leq \dfrac{h^2}{24} (\beta-\alpha)\lVert f^{(2)}\rVert_{\infty}^{[a,b]}$ & 2 \
\hline
Trapèzes & $|E_h^T(f)| \leq \dfrac{h^2}{12} (\beta-\alpha)\lVert f^{(2)}\rVert_{\infty}^{[a,b]}$ & 2 \
\hline
Simpson & $|E_h^S(f)| \leq \dfrac{h^4}{2880} (\beta-\alpha)\lVert f^{(4)}\rVert_{\infty}^{[a,b]}$ & 4 \
\hline
\end{tabular}
\end{table}
\end{document}