Convergence and compactness properties of approximate solutions to elliptic partial differential computed with the hybridized discontinuous Galerkin (HDG) are established. While it is known that solutions computed using the HDG scheme converge at optimal rates to smooth solutions, this does not establish the stability of the method or convergence to solutions with minimal regularity. The compactness and convergence results show that the HDG scheme can be utilized for the solution of nonlinear problems and linear problems with non-smooth coefficients on domains with reentrant corners.

翻译：针对混合化间断伽辽金（HDG）格式计算椭圆型偏微分方程近似解的收敛性与紧致性进行了研究。已知HDG格式能以最优收敛速率逼近光滑解，但该方法在最小正则性条件下的稳定性及收敛性尚未被建立。本文的紧致性与收敛性结果表明，HDG格式可用于求解非线性问题、含非光滑系数的线性问题以及具有重入角区域的问题。