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.

翻译：本文为热方程式引入了超弱的时空 DPG 方法。我们证明变式配方与破损的测试功能相当可靠,并核实实用的DPG 方案的准最佳性。数字实验可以想象出由 DPG 方法内置错误控制驱动的适应性和外观缩放网状精炼的有益性。