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 space-time cylinder, the family of trial spaces that we consider are given as the spans of wavelets-in-time and (locally refined) finite element spaces-in-space. Numerical results illustrate our theoretical findings.

翻译：在这项工作中,为同时用时空变异配方的抛物线进化方程式建造了一个耗资一线的适应求解器。 利用时空圆筒的产品结构,我们所考虑的试验空间系列作为波子时空和(当地改进的)空间空间中有限元素的间隔。 数字结果说明了我们的理论结论。