An adaptive method for parabolic partial differential equations that combines sparse wavelet expansions in time with adaptive low-rank approximations in the spatial variables is constructed and analyzed. The method is shown to converge and satisfy similar complexity bounds as existing adaptive low-rank methods for elliptic problems, establishing its suitability for parabolic problems on high-dimensional spatial domains. The construction also yields computable rigorous a posteriori error bounds for such problems. The results are illustrated by numerical experiments.

翻译：设计并分析了将稀薄的波浪膨胀与空间变量中适应性低位近似值相结合的抛物线部分差异方程的适应性方法。该方法显示,该方法与现有的适应性低位的椭圆问题方法相趋同,并满足了相似的复杂界限,确立了其在高维空间域对抛物线问题的适宜性。该构建还得出了这类问题的事后误差的可计算严格界限。其结果通过数字实验加以说明。