We consider evolutionary systems, i.e. systems of linear partial differential equations arising from the mathematical physics. For these systems there exists a general solution theory in exponentially weighted spaces which can be exploited in the analysis of numerical methods. The numerical method considered in this paper is a discontinuous Galerkin method in time combined with a conforming Galerkin method in space. Building on our recent paper, we improve some of the results, study the dependence of the numerical solution on the weight-parameter, consider a reformulation and post-processing of its numerical solution. As a by-product we provide error estimates for the dG-C0 method. Numerical simulations support the theoretical findings.

翻译：我们考虑演化系统，即源自数学物理的线性偏微分方程组。这类系统在指数加权空间中存在一般解理论，该理论可被用于数值方法的分析。本文考虑的数值方法是时间方向上的间断伽辽金方法结合空间方向上的协调伽辽金方法。基于我们近期的论文，我们改进了部分结果，研究了数值解对权重参数的依赖性，并探讨了数值解的重构与后处理。作为副产品，我们给出了dG-C0方法的误差估计。数值模拟支持理论发现。