Corpus ID: 229371400

A Space-Time DPG Method for the Heat Equation

@article{Diening2020ASD,
  title={A Space-Time DPG Method for the Heat Equation},
  author={L. Diening and J. Storn},
  journal={ArXiv},
  year={2020},
  volume={abs/2012.13229}
}
This paper introduces an ultra-weak space-time DPG method for the heat equation. We prove well-posedness of the variational formulation with broken test functions and verify quasi-optimality of a practical DPG scheme. Numerical experiments visualize beneficial properties of an adaptive and parabolically scaled mesh-refinement driven by the built-in error control of the DPG method. 
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