You may have a need to keep multiple versions of an executable (like java) on your system. Perhaps most of your system will work with Java 8, but one application needs Java 7.

The alternatives program lets you switch from one version to another, quickly.

EDIT: For other reasons you may want to do this, see What is the difference between JAVA_HOME and update-alternatives? and Better way to add alternative using update-alternatives?

From man alternatives:

It is possible for several programs fulfilling the same or similar functions to be installed on a single system at the same time. For example, many systems have several text editors installed at once. This gives choice to the users of a system, allowing each to use a different editor, if desired, but makes it difficult for a program to make a good choice of editor to invoke if the user has not specified a particular preference.

The alternatives system aims to solve this problem. A generic name in the filesystem is shared by all files providing interchangeable functionality. The alternatives system and the system administrator together determine which actual file is referenced by this generic name.

🚨 For working Dockerfile see end of answer. Here's some of the reasoning for how I got there.

I think you'll find that you are not actually using GCC 10 to compile the PETSc code.

Try inserting RUN gcc --version immediately before you clone and build the PETSc repository. I think you'll find that you see something like this:

Step 13/13 : RUN gcc --version
 ---> Running in dc6e2b3c0095
gcc (Ubuntu 9.4.0-1ubuntu1~20.04.2) 9.4.0
Copyright (C) 2019 Free Software Foundation, Inc.
This is free software; see the source for copying conditions.  There is NO
warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

This means that, despite you setting an alternative version of the compiler prior to that it's still reverting to the default compiler. Why?

The reason for this is that something in the subsequent apt-get install is reverting the compiler change. If you change the order of operations to this then you'll find that GCC 10 is in effect when you come to compile PETSc.

RUN apt-get install -y build-essential git python3 openssh-server openssh-client python3-pip ffmpeg libsm6 libxext6 cmake pkg-config \
                       openmpi-bin libopenmpi-dev

RUN update-alternatives --install /usr/bin/gcc gcc /usr/bin/gcc-${COMPILER_VERSION} 60 && \
    update-alternatives --install /usr/bin/g++ g++ /usr/bin/g++-${COMPILER_VERSION} 60 && \
    update-alternatives --install /usr/bin/gfortran gfortran /usr/bin/gfortran-${COMPILER_VERSION} 60

Now you should see this before the clone/compile step:

Step 13/13 : RUN gcc --version
 ---> Running in 77abf17d52bc
gcc (Ubuntu 10.5.0-1ubuntu1~20.04) 10.5.0
Copyright (C) 2020 Free Software Foundation, Inc.
This is free software; see the source for copying conditions.  There is NO
warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

But now there's a snag: there's an error in the PETSc build. It prefers the default compiler version!

My suggestion is to simply remove the first set of update-alternatives commands because they are not having any effect on the subsequent build.

Anyway, here's a complete Dockerfile that should do what you want without duplication. I had to install an updated CMake.

ARG UBUNTU_VERSION=20.04
FROM ubuntu:${UBUNTU_VERSION}

ARG COMPILER_VERSION=10
ARG PETSC_VERSION=v3.18.6

ENV DEBIAN_FRONTEND=noninteractive

RUN apt-get update && \
    apt-get install -y \
        software-properties-common \
        gnupg \
        wget \
        lsb-release
RUN add-apt-repository ppa:ubuntu-toolchain-r/test

# For recent CMake version.
#
RUN wget -O - https://apt.kitware.com/keys/kitware-archive-latest.asc | gpg --dearmor - | tee /usr/share/keyrings/kitware-archive-keyring.gpg >/dev/null
RUN echo "deb [signed-by=/usr/share/keyrings/kitware-archive-keyring.gpg] https://apt.kitware.com/ubuntu $(lsb_release -cs) main" | tee /etc/apt/sources.list.d/kitware.list

RUN apt-get update
RUN apt-get install -y \
        gcc-${COMPILER_VERSION} \
        g++-${COMPILER_VERSION} \
        gfortran-${COMPILER_VERSION} \
        build-essential \
        git \
        python3 \
        openssh-server \
        openssh-client \
        python3-pip \
        ffmpeg \
        libsm6 \
        libxext6 \
        cmake \
        pkg-config \
        openmpi-bin \
        libopenmpi-dev

RUN update-alternatives --install /usr/bin/gcc gcc /usr/bin/gcc-${COMPILER_VERSION} 60 && \
    update-alternatives --install /usr/bin/g++ g++ /usr/bin/g++-${COMPILER_VERSION} 60 && \
    update-alternatives --install /usr/bin/gfortran gfortran /usr/bin/gfortran-${COMPILER_VERSION} 60

RUN python3 -m pip install pytest numpy h5py pathlib requests pandas matplotlib plotly scikit-learn PyYAML Pillow vtk types-PyYAML pytest-cov

RUN echo "Using PETSC_VERSION: ${PETSC_VERSION}"
RUN git clone -b ${PETSC_VERSION} https://gitlab.com/petsc/petsc.git /petsc && \
    cd /petsc && \
    ./configure \
        PETSC_ARCH=linux-gnu \
        --with-fc=gfortran --with-cc=gcc --with-cxx=g++ \
        --with-fortran-bindings \
        --download-openmpi \
        --with-mpi-f90module-visibility=1 \
        --download-fftw \
        --download-hdf5 \
        --download-hdf5-fortran-bindings \
        --download-fblaslapack \
        --download-scalapack \
        --download-ml \
        --download-zlib && \
    make all

ENV PETSC_DIR /petsc
ENV PETSC_ARCH linux-gnu

ENV OMPI_ALLOW_RUN_AS_ROOT 1
ENV OMPI_ALLOW_RUN_AS_ROOT_CONFIRM 1