# 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.

#### 4 Citations

Analysis of Backward Euler Primal DPG Methods

- Mathematics, Computer Science
- ArXiv
- 2021

Optimal error estimates are shown in a natural norm and in the L2{L^{2}} norm of the field variable for the heat equation of a primal DPG formulation of a class of parabolic problems. Expand

A wavelet-in-time, finite element-in-space adaptive method for parabolic evolution equations

- Mathematics, Computer Science
- ArXiv
- 2021

In this work, an r-linearly converging adaptive solver is constructed for parabolic evolution equations in a simultaneous space-time variational formulation. Exploiting the product structure of the… Expand

Minimal residual space-time discretizations of parabolic equations: Asymmetric spatial operators

- Computer Science, Mathematics
- ArXiv
- 2021

A minimal residual discretization of a simultaneous spacetime variational formulation of parabolic evolution equations is considered and quasi-optimality of the numerical approximations without assuming symmetry of the spatial part of the differential operator is shown. Expand

Optimal local approximation spaces for parabolic problems

- Mathematics, Computer Science
- ArXiv
- 2020

Local space-time approximation spaces for parabolic problems that are optimal in the sense of Kolmogorov and may be employed in multiscale and domain decomposition methods are proposed and derive rigorous local and global a priori error bounds. Expand

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