COMPLETELY UNSUPPORTED way to build rstudio from the v1.3-patches branch with QT 5.15 for ubuntu/20.04 focal & R 4.0. Put both files in the same directory. Note a docker install is needed for this to work.

build_rstudio_focal.sh

#!/bin/bash -ex
git_branch="v1.3-patch"
git_base="https://github.com/rstudio/rstudio"
QT_VERSION=5.15.0
now=$(date +"%m%d%Y%H%M")
#docker build --pull --no-cache -f Dockerfile.focal-amd64 -t rstudio:focal-amd64 .
# following from https://stackoverflow.com/a/246128
SOURCE="${BASH_SOURCE[0]}"
while [ -h "$SOURCE" ]; do # resolve $SOURCE until the file is no longer a symlink
  DIR="$( cd -P "$( dirname "$SOURCE" )" >/dev/null 2>&1 && pwd )"
  SOURCE="$(readlink "$SOURCE")"
  [[ $SOURCE != /* ]] && SOURCE="$DIR/$SOURCE" # if $SOURCE was a relative symlink, we need to resolve it relative to the path where the symlink file was located
done
DIR="$( cd -P "$( dirname "$SOURCE" )" >/dev/null 2>&1 && pwd )"

if [[ -e "rstudio" ]]; then
        cd rstudio
        git pull
        git reset --hard
        patch -p1 --forward --force <"$DIR"/rstudio-1.3.patch || true
        echo "updated git"  
else
        git clone -b $git_branch --depth=1 $git_base
        cd rstudio
        patch -p1 --forward --force <"$DIR"/rstudio-1.3.patch || true
        echo "recreated git"
fi
#QT_VERSION=$(grep -oP '(?<=QT_VERSION=)(\s+)?\K([^ ]*)' rstudio/docker/jenkins/Dockerfile.focal-amd64)
sed -i "s/\bQT_VERSION=[^ ]*/QT_VERSION=$QT_VERSION/" "$DIR"/rstudio/docker/jenkins/Dockerfile.focal-amd64
sed -i "s/QT_CANDIDATES 5/QT_CANDIDATES $QT_VERSION 5/g" "$DIR"/rstudio/src/cpp/desktop/CMakeLists.txt
cd "$DIR"/rstudio/docker
./docker-compile.sh focal-amd64 desktop 1.3."$now"

rstudio-1.3.patch

diff '--exclude=.git' -Npaur a/dependencies/common/install-common b/dependencies/common/install-common
--- a/dependencies/common/install-common	2020-05-11 22:11:46.193261644 -0400
+++ b/dependencies/common/install-common	2020-05-11 22:13:49.039501487 -0400
@@ -19,7 +19,7 @@ set -e
 
 ./install-dictionaries
 ./install-mathjax
-./install-boost
+#./install-boost
 ./install-pandoc
 ./install-packages
 ./install-sentry-cli
diff '--exclude=.git' -Npaur a/dependencies/common/install-qt.sh b/dependencies/common/install-qt.sh
--- a/dependencies/common/install-qt.sh	2020-05-11 22:11:46.194261629 -0400
+++ b/dependencies/common/install-qt.sh	2020-05-11 22:13:49.039501487 -0400
@@ -208,7 +208,7 @@ function compute_url(){
     if [[ "${COMPONENT}" =~ "qtcreator" ]]; then
 
         REMOTE_BASE="tools_qtcreator/qt.tools.qtcreator"
-        REMOTE_PATH="$(${CURL} ${BASE_URL}/${REMOTE_BASE}/ | grep -o -E "${VERSION}[0-9\-]*${COMPONENT}\.7z" | tail -1)"
+        REMOTE_PATH="$(${CURL} ${BASE_URL}/${REMOTE_BASE}/ | grep -o -E "${VERSION}[0-9\-]*${COMPONENT}\.7z" | head -1)"
 
         if [ ! -z "${REMOTE_PATH}" ]; then
             echo "${BASE_URL}/${REMOTE_BASE}/${REMOTE_PATH}"
@@ -232,9 +232,9 @@ function compute_url(){
             if [[ "${HOST_OS}" == "linux_x64" && "${VERSION}" == "5.12.8" ]]; then
                 # Qt 5.12.8 Linux release has multiple files in release folders; install the correct one!
                 # https://github.com/rstudio/rstudio/issues/6782
-                REMOTE_PATH="$(${CURL} ${BASE_URL}/${REMOTE_BASE}/ | grep -o -E "5\.12\.8\-0\-20200405[[:alnum:]_.\-]*7z" | grep "${COMPONENT}" | tail -1)"
+                REMOTE_PATH="$(${CURL} ${BASE_URL}/${REMOTE_BASE}/ | grep -o -E "5\.12\.8\-0\-20200405[[:alnum:]_.\-]*7z" | grep "${COMPONENT}" | head -1)"
             else
-                REMOTE_PATH="$(${CURL} ${BASE_URL}/${REMOTE_BASE}/ | grep -o -E "[[:alnum:]_.\-]*7z" | grep "${COMPONENT}" | tail -1)"
+                REMOTE_PATH="$(${CURL} ${BASE_URL}/${REMOTE_BASE}/ | grep -o -E "[[:alnum:]_.\-]*7z" | grep "${COMPONENT}" | head -1)"
             fi
             if [ ! -z "${REMOTE_PATH}" ]; then
                 echo "${BASE_URL}/${REMOTE_BASE}/${REMOTE_PATH}"
diff '--exclude=.git' -Npaur a/docker/jenkins/Dockerfile.focal-amd64 b/docker/jenkins/Dockerfile.focal-amd64
--- a/docker/jenkins/Dockerfile.focal-amd64	1969-12-31 19:00:00.000000000 -0500
+++ b/docker/jenkins/Dockerfile.focal-amd64	2020-05-11 22:13:49.040501473 -0400
@@ -0,0 +1,114 @@
+FROM ubuntu:focal
+
+ARG AWS_REGION=us-east-1
+
+# install needed packages. replace httpredir apt source with cloudfront
+RUN set -x \
+    && sed -i "s/archive.ubuntu.com/$AWS_REGION.ec2.archive.ubuntu.com/" /etc/apt/sources.list \
+    && export DEBIAN_FRONTEND=noninteractive \
+    && apt-get update \
+    && apt-get install -y gnupg \
+    && apt-key adv --keyserver keyserver.ubuntu.com --recv-keys 0x51716619e084dab9 \
+    && echo 'deb http://cran.rstudio.com/bin/linux/ubuntu focal-cran40/' >> /etc/apt/sources.list \
+    && apt-get update
+
+# add ppa repository so we can install java 8 (not in any official repo for bionic)
+RUN apt-get update \
+  && apt-get install -y software-properties-common \
+  && add-apt-repository ppa:openjdk-r/ppa
+
+RUN apt-get update && \
+    export DEBIAN_FRONTEND=noninteractive && \
+    apt-get install -y \
+    ant \
+    autoconf \
+    build-essential \
+    clang \
+    cmake \
+    curl \
+    debsigs \
+    dpkg-sig \
+    expect \
+    fakeroot \
+    git-core \
+    libattr1-dev \
+    libacl1-dev \
+    libboost-all-dev \
+    libbz2-dev \
+    libcap-dev \
+    libcurl4-openssl-dev \
+    libfuse2 \
+    libgpg-error0 \
+    libgtk-3-0 \
+    libgl1-mesa-dev \
+    libegl1-mesa \
+    libpam-dev \
+    libpango1.0-dev \
+    libuser1-dev \
+    libssl1.1 libssl-dev \
+    libxslt1-dev \
+    lsof \
+    openjdk-11-jdk \
+    patchelf \
+    p7zip-full \
+    pkg-config \
+    python \
+    r-base \
+    sudo \
+    unzip \
+    uuid-dev \
+    valgrind \
+    wget \
+    yarnpkg \
+    zlib1g-dev
+
+# ensure we use the java 11 compiler
+#RUN update-alternatives --set java /usr/lib/jvm/java-11-openjdk-amd64/jre/bin/java
+
+## build patchelf
+#RUN cd /tmp \
+#    && wget https://github.com/NixOS/patchelf/archive/0.10.tar.gz \
+#    && mv 0.10.tar.gz patchelf-0.10.tar.gz \
+#    && tar xzvf patchelf-0.10.tar.gz \
+#    && cd patchelf-0.10 \
+#    && ./bootstrap.sh \
+#    && ./configure \
+#    && make \
+#    && make install
+
+## run install-boost twice - boost exits 1 even though it has installed good enough for our uses.
+## https://github.com/rstudio/rstudio/blob/master/vagrant/provision-primary-user.sh#L12-L15
+#COPY dependencies/common/install-boost /tmp/
+#RUN bash /tmp/install-boost || bash /tmp/install-boost
+RUN mkdir /opt/rstudio-tools
+
+# set github login from build argument if defined
+ARG GITHUB_LOGIN
+ENV RSTUDIO_GITHUB_LOGIN=$GITHUB_LOGIN
+
+# install cmake
+COPY package/linux/install-dependencies /tmp/
+RUN /bin/bash /tmp/install-dependencies
+
+# install crashpad and its dependencies
+COPY dependencies/common/install-crashpad /tmp/
+RUN bash /tmp/install-crashpad bionic
+
+# install common dependencies
+RUN mkdir -p /opt/rstudio-tools/dependencies/common
+COPY dependencies/common/ /opt/rstudio-tools/dependencies/common/
+RUN cd /opt/rstudio-tools/dependencies/common && /bin/bash ./install-common
+
+# install Qt SDK
+COPY dependencies/common/install-qt.sh /tmp/
+COPY dependencies/linux/install-qt-linux /tmp/
+RUN export QT_VERSION=5.14.2 && \
+    cd /tmp && /bin/bash ./install-qt-linux
+
+# create jenkins user, make sudo. try to keep this toward the bottom for less cache busting
+ARG JENKINS_GID=999
+ARG JENKINS_UID=999
+RUN groupadd -g $JENKINS_GID jenkins && \
+    useradd -m -d /var/lib/jenkins -u $JENKINS_UID -g jenkins jenkins && \
+    echo "jenkins ALL=(ALL) NOPASSWD: ALL" >> /etc/sudoers
+
diff '--exclude=.git' -Npaur a/src/cpp/CMakeLists.txt b/src/cpp/CMakeLists.txt
--- a/src/cpp/CMakeLists.txt	2020-05-11 22:11:46.238260988 -0400
+++ b/src/cpp/CMakeLists.txt	2020-05-11 22:13:49.040501473 -0400
@@ -272,7 +272,7 @@ endif()
 # allow opt-in to using Boost.Signals2
 # TODO: remove this in RStudio v1.3 and port to signals2
 if(NOT RSTUDIO_BOOST_SIGNALS_VERSION)
-   if (Boost_VERSION LESS 106900)
+   if (BOOST_VERSION LESS 106900)
       set(RSTUDIO_BOOST_SIGNALS_VERSION 1)
    else()
       set(RSTUDIO_BOOST_SIGNALS_VERSION 2)
diff '--exclude=.git' -Npaur a/src/cpp/desktop/install/LinuxInstallQt.sh.in b/src/cpp/desktop/install/LinuxInstallQt.sh.in
--- a/src/cpp/desktop/install/LinuxInstallQt.sh.in	2020-05-11 22:11:46.290260231 -0400
+++ b/src/cpp/desktop/install/LinuxInstallQt.sh.in	2020-05-11 22:14:37.932815314 -0400
@@ -17,13 +17,13 @@ COMPONENTS=(
 	lib/libQt5Positioning.so.5
 	lib/libQt5PrintSupport.so.5
 	lib/libQt5Qml.so.5
+        lib/libQt5QmlModels.so.5
 	lib/libQt5Quick.so.5
 	lib/libQt5QuickWidgets.so.5
 	lib/libQt5Sensors.so.5
 	lib/libQt5Sql.so.5
 	lib/libQt5Svg.so.5
 	lib/libQt5WaylandClient.so.5
-	lib/libQt5WaylandCompositor.so.5
 	lib/libQt5WebChannel.so.5
 	lib/libQt5WebEngine.so.5
 	lib/libQt5WebEngineCore.so.5