We study the numerical approximation of a coupled hyperbolic-parabolic system by a family of discontinuous Galerkin space-time finite element methods. The model is rewritten as a first-order evolutionary problem that is treated by the unified abstract solution theory of R.\ Picard. To preserve the mathematical structure of the evolutionary equation on the fully discrete level, suitable generalizations of the distribution gradient and divergence operators on broken polynomial spaces on which the discontinuous Galerkin approach is built on are defined. Well-posedness of the fully discrete problem and error estimates for the discontinuous Galerkin approximation in space and time are proved.

翻译：研究了一类耦合双曲-抛物系统由间断伽辽金时空有限元方法族给出的数值逼近。该模型被重写为一阶演化问题，并采用R. Picard的统一抽象解理论进行处理。为了在全离散层面保持演化方程的数学结构，定义了间断多项式空间上分布梯度算子和散度算子的适当推广形式，这些空间正是间断伽辽金方法构建的基础。证明了全离散问题的适定性，并给出了时空间断伽辽金逼近的误差估计。