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. For the discretization in space, generalizations of the distribution gradient and divergence operators on broken polynomial spaces are defined. Since their skew-selfadjointness is perturbed by boundary surface integrals, adjustments are introduced such that the skew-selfadjointness of the first-order differential operator in space is recovered. Well-posedness of the fully discrete problem and error estimates for the discontinuous Galerkin approximation in space and time are proved.

翻译：本文研究了一类间断伽辽金时空有限元方法对耦合双曲-抛物系统的数值逼近问题。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。针对空间离散化，我们定义了破碎多项式空间上分布梯度与散度算子的推广形式。由于这些算子的斜自伴性受到边界面积分的扰动，我们引入了相应调整以恢复空间一阶微分算子的斜自伴特性。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。