In this paper, we study the convergence of adaptive mixed interior penalty discontinuous Galerkin method for -elliptic problems. We first get the mixed model of -elliptic problem by introducing a new intermediate variable. Then we discuss the continuous variational problem and discrete variational problem, which based on interior penalty discontinuous Galerkin approximation. Next, we construct the corresponding posteriori error indicator, and prove the contraction of the summation of the energy error and the scaled error indicator. At last, we confirm and illustrate the theoretical result through some numerical experiments.

中文翻译：

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[式略]-椭圆问题的自适应混合内罚间断伽辽金方法的收敛性


本文研究了椭圆问题的自适应混合内罚间断伽辽金方法的收敛性。我们首先通过引入一个新的中间变量得到-椭圆问题的混合模型。然后讨论了基于内罚间断伽辽金近似的连续变分问题和离散变分问题。接下来，我们构造相应的后验误差指标，并证明能量误差和缩放误差指标之和的收缩。最后，我们通过数值实验验证并说明了理论结果。