A Space-Time DPG Method for the Heat Equation

TL;DR

This paper presents an ultra-weak space-time DPG method for the heat equation, demonstrating well-posedness, quasi-optimality, and effective adaptive mesh refinement through numerical experiments.

Contribution

It introduces a novel space-time DPG formulation for the heat equation with proven theoretical properties and practical adaptive refinement strategies.

Findings

Proven well-posedness of the variational formulation

Demonstrated quasi-optimality of the DPG scheme

Numerical experiments show effective adaptive mesh refinement

Abstract

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.