In (Dzanic, J. Comp. Phys., 508:113010, 2024), a limiting approach for high-order discontinuous Galerkin schemes was introduced which allowed for imposing constraints on the solution continuously (i.e., everywhere within the element). While exact for linear constraint functionals, this approach only imposed a sufficient (but not the minimum necessary) amount of limiting for nonlinear constraint functionals. This short note shows how this limiting approach can be extended to allow exactness for general nonlinear quasiconcave constraint functionals through a nonlinear limiting procedure, reducing unnecessary numerical dissipation. Some examples are shown for nonlinear pressure and entropy constraints in the compressible gas dynamics equations, where both analytic and iterative approaches are used.

翻译：在(Dzanic, J. Comp. Phys., 508:113010, 2024)中，作者提出了一种针对高阶间断伽辽金格式的极限方法，该方法允许对解施加连续约束（即在单元内处处满足约束条件）。虽然该方法对于线性约束泛函是精确的，但对于非线性约束泛函仅施加了充分（而非最小必要）的极限量。本短篇注记展示了如何通过非线性极限过程扩展该极限方法，使其能够精确处理一般非线性拟凹约束泛函，从而减少不必要的数值耗散。文中以可压缩气体动力学方程中的非线性压力和熵约束为例，展示了解析与迭代两种求解方法的应用。