How can I run a flutter web app using Docker?

I have implemented my first (running) web app using Flutter and I would now to deploy it using Docker (which is rather new to me) to run it.

My folder structure is as follows: ${workdir}/Dockerfile, ${workdir}/docker-compose.yaml and ${workdir}/myprog where the latter is my Intellij project directory, thus containing the pubspec.yaml-file. The latter is the same as the demo-file.

Dockerfile is as follows:

FROM ubuntu:20.04

# Prerequisites
RUN apt-get update && apt-get install -y unzip xz-utils git openssh-client curl && apt-get upgrade -y && rm -rf /var/cache/apt

# Install flutter beta
RUN curl -L https://storage.googleapis.com/flutter_infra/releases/beta/linux/flutter_linux_1.22.0-12.1.pre-beta.tar.xz | tar -C /opt -xJ

ENV PATH "$PATH:/opt/flutter/bin"

# Enable web capabilities
RUN flutter config --enable-web
RUN flutter upgrade
RUN flutter pub global activate webdev
RUN flutter doctor

# Initialize web-app
WORKDIR /opt/web

# Copy it into docker container
COPY ./myprog/ ./

and docker-compose.yaml file is

version: '3.1'
services:
  webapp:
    container_name: myprog
    restart: always
    image: myprog
    ports:
      - 5001:5001 
    build:
      context: ./
    volumes:
      - /var/run/docker.sock:/var/run/docker.sock
    command: ["flutter", "pub", "global", "run", "webdev", "serve", "0.0.0.0:5001"]

I successfully build it using docker-compose -f docker-compose.yaml build, but running it using docker-compose -f docker-compose.yaml up fails with the following error message

myprog    | webdev could not run for this project.
myprog    | Could not find a file named "pubspec.yaml" in "/opt/flutter/.pub-cache/hosted/pub.dartlang.org/flutter_keyboard_visibility-3.2.2".
myprog    | pub finished with exit code 78

The full path of the pubspec.yaml is /opt/web/pubspec.yaml. How can I fix this issue?