1

I am trying to write this mathematical expression correctly and systematically. I need some help, please:

\begin{equation} \label{58}
\begin{array}{l}
\alpha_{\mathcal{A}}\|w_n-w_n^{hk}\|^2_V \\
&\leq \langle \mathcal{A}\varepsilon(w_n)-\mathcal{A}^l\varepsilon(w_n^{hk}),\varepsilon(w_n-v_n^h) \rangle_{\mathcal{H}}+ \langle\mathcal{A}^l\varepsilon(w_n),\varepsilon(v_n^h-w_n)\rangle_{\mathcal{H}} +\langle F_n,w_n-v_n^h\rangle_V\\
&+ \langle\mathcal{B}^l(\varepsilon(u_n)),\varepsilon(w_n^{hk}-w_n)\rangle_{\mathcal{H}} + \langle\mathcal{B}^l(\varepsilon(u_n^{hk})),\varepsilon(v_n^h -w_n^{hk})\rangle_{\mathcal{H}} +\langle\int_{0}^t \mathcal{G}^l(t-s)u_n \mathrm{d}s,\varepsilon(w_n^{hk}-
w_n)\rangle_{\mathcal{H}}  \\

& + \langle\int_{0}^t \mathcal{G}^l(t-s)u_n^{hk}\mathrm{d}s,\varepsilon(v_n^h-w_n^{hk})\rangle_{\mathcal{H}} +
\langle(\mathcal{P^*})^l\nabla \varphi_n,\varepsilon(w_n^{hk}-w_n)\rangle_{\mathcal{H}} + \langle(\mathcal{P^*})^l\nabla \varphi_n^{hk},\varepsilon(v_n^h-w_n^{hk})\rangle_{\mathcal{H}}  \\

&-\langle \mathcal{C}^l\theta_n,\varepsilon(w_n^{hk}-w_n)\rangle_{\mathcal{H}}- \langle \mathcal{C}^l\theta_n^{hk},\varepsilon(v_n^h-w_n^{hk})\rangle_{\mathcal{H}} +
 \int_{\Gamma_3} j_{\nu}^0(w_{n\nu};w_{n\nu}^{hk}-w_{n\nu})+j_\nu^0(w_{n\nu}^{hk};v_{n\nu}^h-w_{n\nu}^{hk}) \mathrm{d}a  \\  
 
&+\int_{\Gamma_3} j_{\tau}^0(w_{n\tau};w_{n\nu}^{hk}-w_{n\nu})+j_\tau^0(w_{n\tau}^{hk};v_{n\nu}^h-w_{n\nu}^{hk}) \mathrm{d}s  \\
&\leq \langle \mathcal{A}^l\varepsilon(w_n)-\mathcal{A}^l\varepsilon(w_n^{hk}),\varepsilon(w_n-v_n^h) \rangle_{\mathcal{H}}   +\langle\mathcal{A}^l\varepsilon(w_n),\varepsilon(v_n^h-w_n)\rangle_{\mathcal{H}} + \langle\mathcal{B}^l(\varepsilon(u_n^{hk})),\varepsilon(v_n^h-w_n)\rangle_{\mathcal{H}} \\

&+ \langle\mathcal{B}^l(\varepsilon(u_n)) -\mathcal{B}^l(\varepsilon(u_n^{hk}))  ,\varepsilon(w_n^{hk} -w_n)\rangle_{\mathcal{H}} +\langle\int_{0}^t \mathcal{G}^l(t-s)u_n^{hk} \mathrm{d}s,\varepsilon(v_n^h-w_n)\rangle_{\mathcal{H}} \\

&+ \langle\int_{0}^t \mathcal{G}^l(t-s)u_n \mathrm{d}s-\int_{0}^t \mathcal{G}^l(t-s)u_n^{hk} \mathrm{d}s,\varepsilon(w_n^{hk}-w_n)\rangle_{\mathcal{H}}+ \langle(\mathcal{P^*})^l\nabla \varphi_n -( \mathcal{P^*})^l\nabla \varphi_n^{hk},\varepsilon(w_n^{hk}-w_n)\rangle_{\mathcal{H}}\\

&+ \langle(\mathcal{P^*})^l\nabla \varphi_n^{hk},\varepsilon(v_n^h-w_n)\rangle_{\mathcal{H}} - \langle \mathcal{C}^l\theta_n^{hk},\varepsilon(v_n^h-w_n)\rangle_{\mathcal{H}} -\langle \mathcal{C}^l\theta_n- \mathcal{C}^l\theta_n^{hk},\varepsilon(w_n^{hk}-w_n)\rangle_{\mathcal{H}} \\

&+ \langle F_n,w_n-v_n^h\rangle_V + 
\int_{\Gamma_3} j_{\nu}^0(w_{n\nu};w_{n\nu}^{hk}-w_{n\nu})+j_\nu^0(w_{n\nu}^{hk};v_{n\nu}^h-w_{n\nu}^{hk}) \mathrm{d}a \\

&+\int_{\Gamma_3} j_{\tau}^0(w_{n\tau};w_{n\nu}^{hk}-w_{n\nu})+j_\tau^0(w_{n\tau}^{hk};v_{n\nu}^h-w_{n\nu}^{hk}) \mathrm{d}a \\

&+
\int_{\Gamma_3} j_{\nu}^0(w_{n\nu}^{hk};v_n^h-w_n) \mathrm{d}a + j_\tau^0(w_{n\tau}^{hk};v_n^h-w_{n\nu}) \mathrm{d}a
\end{array}
\end{equation}
3
  • You've defined an array with one left aligned column, but you are using more than one column. If suggest to use split instead of an array. See the amsmath manual for more information.
    – cabohah
    Feb 28 at 12:37
  • Have you considered using landscape mode equation? it might be easier to read.
    – anis
    Feb 28 at 12:48
  • Note that blank lines aren't allowed in display environments.
    – Teepeemm
    Feb 28 at 13:29

3 Answers 3

3

A variant with array. But notice \innpr, in particular around integrals.

\documentclass{article}
\usepackage{amsmath, amssymb,array,mathtools}

\DeclarePairedDelimiter{\innpr}{\langle}{\rangle}

\begin{document}

\begin{equation} \label{eq:58}
\setlength{\arraycolsep}{0pt}
\renewcommand{\arraystretch}{2}
\begin{array}{
  l<{\vphantom{\displaystyle\int_0^t}}
  >{\quad{}}r<{{}}
  >{\quad{}}r<{{}}
  >{\displaystyle}l
}
\multicolumn{4}{l}{\displaystyle\alpha_{\mathcal{A}}\|w_n-w_n^{hk}\|^2_V} \\
&\leq&
  \multicolumn{2}{l}{\displaystyle
    \innpr{ \mathcal{A}\varepsilon(w_n)-\mathcal{A}^l\varepsilon(w_n^{hk}),
    \varepsilon(w_n-v_n^h) }_{\mathcal{H}}
    +\innpr{\mathcal{A}^l\varepsilon(w_n),\varepsilon(v_n^h-w_n)}_{\mathcal{H}}}
\\
&&+& \innpr{ F_n,w_n-v_n^h}_V \\
&&+& \innpr{\mathcal{B}^l(\varepsilon(u_n)),\varepsilon(w_n^{hk}-w_n)}_{\mathcal{H}} + \innpr{\mathcal{B}^l(\varepsilon(u_n^{hk})),\varepsilon(v_n^h -w_n^{hk})}_{\mathcal{H}} \\
&&+& \innpr[\Big]{\int_{0}^t \mathcal{G}^l(t-s)u_n \, ds,\varepsilon(w_n^{hk}-w_n)}_{\mathcal{H}} \\
&&+& \innpr[\Big]{\int_{0}^t \mathcal{G}^l(t-s)u_n^{hk}\, ds,\varepsilon(v_n^h-w_n^{hk})}_{\mathcal{H}} \\
&&+& \innpr{(\mathcal{P^*})^l\nabla \varphi_n,\varepsilon(w_n^{hk}-w_n)}_{\mathcal{H}} + \innpr{(\mathcal{P^*})^l\nabla \varphi_n^{hk},\varepsilon(v_n^h-w_n^{hk})}_{\mathcal{H}} \\
&&-& \innpr{ \mathcal{C}^l\theta_n,\varepsilon(w_n^{hk}-w_n)}_{\mathcal{H}}- \innpr{ \mathcal{C}^l\theta_n^{hk},\varepsilon(v_n^h-w_n^{hk})}_{\mathcal{H}} \\
&&+& \int_{\Gamma_3} j_{\nu}^0(w_{n\nu};w_{n\nu}^{hk}-w_{n\nu})+j_\nu^0(w_{n\nu}^{hk};v_{n\nu}^h-w_{n\nu}^{hk}) \, da  \\
&&+& \int_{\Gamma_3} j_{\tau}^0(w_{n\tau};w_{n\nu}^{hk}-w_{n\nu})+j_\tau^0(w_{n\tau}^{hk};v_{n\nu}^h-w_{n\nu}^{hk}) \, da \\
&&+& \int_{\Gamma_3} j_{\nu}^0(w_{n\nu}^{hk};v_n^h-w_n) \, da + j_\tau^0(w_{n\tau}^{hk};v_n^h-w_{n\nu}) \, da
\end{array}
\end{equation} 

\end{document}

enter image description here

Use \begin{array}[b] if you want the equation number to be at the bottom.

enter image description here

2

Some suggestions after @Sebastiano 's answer:

a) I would much prefer it if lines were equidistant. A (crude) way to achieve this would be by using a \phantom{\int_0^t} in the shorter lines.

b) I would probably prefer it if the \leq was placed on the first line rather than on the second.

\documentclass{article}
\usepackage{amsmath, amssymb}

\begin{document}

\begin{equation} \label{eq:58}
\begin{split}
\alpha_{\mathcal{A}}&\|w_n-w_n^{hk}\|^2_V \leq\\
&  \langle \mathcal{A}\varepsilon(w_n)-\mathcal{A}^l\varepsilon(w_n^{hk}),\varepsilon(w_n-v_n^h) \rangle_{\mathcal{H}}+ \langle\mathcal{A}^l\varepsilon(w_n),\varepsilon(v_n^h-w_n)\rangle_{\mathcal{H}}  \phantom{\int_0^t} \\
&+ \langle F_n,w_n-v_n^h\rangle_V \phantom{\int_0^t}\\
&+ \langle\mathcal{B}^l(\varepsilon(u_n)),\varepsilon(w_n^{hk}-w_n)\rangle_{\mathcal{H}} + \langle\mathcal{B}^l(\varepsilon(u_n^{hk})),\varepsilon(v_n^h -w_n^{hk})\rangle_{\mathcal{H}} \phantom{\int_0^t}\\
&+ \langle\int_{0}^t \mathcal{G}^l(t-s)u_n \, ds,\varepsilon(w_n^{hk}-w_n)\rangle_{\mathcal{H}} \\
&+ \langle\int_{0}^t \mathcal{G}^l(t-s)u_n^{hk}\, ds,\varepsilon(v_n^h-w_n^{hk})\rangle_{\mathcal{H}} \\
&+ \langle(\mathcal{P^*})^l\nabla \varphi_n,\varepsilon(w_n^{hk}-w_n)\rangle_{\mathcal{H}} + \langle(\mathcal{P^*})^l\nabla \varphi_n^{hk},\varepsilon(v_n^h-w_n^{hk})\rangle_{\mathcal{H}} \phantom{\int_0^t}\\
&- \langle \mathcal{C}^l\theta_n,\varepsilon(w_n^{hk}-w_n)\rangle_{\mathcal{H}}- \langle \mathcal{C}^l\theta_n^{hk},\varepsilon(v_n^h-w_n^{hk})\rangle_{\mathcal{H}}  \phantom{\int_0^t}\\
&+ \int_{\Gamma_3} j_{\nu}^0(w_{n\nu};w_{n\nu}^{hk}-w_{n\nu})+j_\nu^0(w_{n\nu}^{hk};v_{n\nu}^h-w_{n\nu}^{hk}) \, da  \\
&+ \int_{\Gamma_3} j_{\tau}^0(w_{n\tau};w_{n\nu}^{hk}-w_{n\nu})+j_\tau^0(w_{n\tau}^{hk};v_{n\nu}^h-w_{n\nu}^{hk}) \, da \\
&+ \int_{\Gamma_3} j_{\nu}^0(w_{n\nu}^{hk};v_n^h-w_n) \, da + j_\tau^0(w_{n\tau}^{hk};v_n^h-w_{n\nu}) \, da
\end{split}
\end{equation} 

\end{document}

enter image description here

1

Using a split enviroment (see the comment of @cabohah).

\documentclass{article}
\usepackage{amsmath, amssymb}

\begin{document}

\begin{equation} \label{eq:58}
\begin{split}
&\alpha_{\mathcal{A}}\|w_n-w_n^{hk}\|^2_V \\
&\leq \langle \mathcal{A}\varepsilon(w_n)-\mathcal{A}^l\varepsilon(w_n^{hk}),\varepsilon(w_n-v_n^h) \rangle_{\mathcal{H}}+ \langle\mathcal{A}^l\varepsilon(w_n),\varepsilon(v_n^h-w_n)\rangle_{\mathcal{H}} \\
&+ \langle F_n,w_n-v_n^h\rangle_V \\
&+ \langle\mathcal{B}^l(\varepsilon(u_n)),\varepsilon(w_n^{hk}-w_n)\rangle_{\mathcal{H}} + \langle\mathcal{B}^l(\varepsilon(u_n^{hk})),\varepsilon(v_n^h -w_n^{hk})\rangle_{\mathcal{H}} \\
&+ \langle\int_{0}^t \mathcal{G}^l(t-s)u_n \, ds,\varepsilon(w_n^{hk}-w_n)\rangle_{\mathcal{H}} \\
&+ \langle\int_{0}^t \mathcal{G}^l(t-s)u_n^{hk}\, ds,\varepsilon(v_n^h-w_n^{hk})\rangle_{\mathcal{H}} \\
&+ \langle(\mathcal{P^*})^l\nabla \varphi_n,\varepsilon(w_n^{hk}-w_n)\rangle_{\mathcal{H}} + \langle(\mathcal{P^*})^l\nabla \varphi_n^{hk},\varepsilon(v_n^h-w_n^{hk})\rangle_{\mathcal{H}} \\
&- \langle \mathcal{C}^l\theta_n,\varepsilon(w_n^{hk}-w_n)\rangle_{\mathcal{H}}- \langle \mathcal{C}^l\theta_n^{hk},\varepsilon(v_n^h-w_n^{hk})\rangle_{\mathcal{H}} \\
&+ \int_{\Gamma_3} j_{\nu}^0(w_{n\nu};w_{n\nu}^{hk}-w_{n\nu})+j_\nu^0(w_{n\nu}^{hk};v_{n\nu}^h-w_{n\nu}^{hk}) \, da  \\
&+ \int_{\Gamma_3} j_{\tau}^0(w_{n\tau};w_{n\nu}^{hk}-w_{n\nu})+j_\tau^0(w_{n\tau}^{hk};v_{n\nu}^h-w_{n\nu}^{hk}) \, da \\
&+ \int_{\Gamma_3} j_{\nu}^0(w_{n\nu}^{hk};v_n^h-w_n) \, da + j_\tau^0(w_{n\tau}^{hk};v_n^h-w_{n\nu}) \, da
\end{split}
\end{equation} 

\end{document}

enter image description here

1
  • @MadyYuvi Very kind MadyYuvi I have taken only the suggestion of cabohah.
    – Sebastiano
    Apr 22 at 11:32

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