In this note we consider a parabolic evolution equation in a polygonal space-time cylinder. We show, that the elliptic part is given by a m-accretive mapping from L q (Ω) → L q (Ω). Therefore we can apply the theory of nonlinear semigroups in Banach spaces in order to get regularity results in time and space. The second part of the paper deals with the numerical solution of the problem. It is dedicated to the application of the space-time discontinuous Galerkin method (STDGM). It means that both in space as well as in time discontinuous piecewise polynomial approximations of the solution are used. We concentrate to the theoretical analysis of the error estimation.

中文翻译：

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多边形时空圆柱中具有非线性牛顿边界条件的半线性抛物初边值问题的间断Galerkin方法的正则性结果及数值解

在本说明中，我们考虑了多边形时空圆柱中的抛物线演化方程。我们证明，椭圆部分由来自的 m-accretive 映射给出大号 q (Ω) →大号 q (Ω)。因此我们可以应用巴拿赫空间中的非线性半群理论来得到时间和空间上的规律性结果。论文的第二部分涉及问题的数值解。它专门用于时空不连续伽辽金方法（STDGM）的应用。这意味着在空间和时间上都使用解的不连续分段多项式近似。我们专注于误差估计的理论分析。