标题： 一种保持界限的保守增强伽辽金方法用于椭圆问题 显示英文标题

标题： A bound-preserving and conservative enriched Galerkin method for elliptic problems

摘要： 我们提出了一种局部保守的增强伽辽金方案，该方案尊重椭圆问题的离散最大值原理。 为此，我们对离散解的跳跃进行显著的过惩罚以获得最优收敛性。 为了避免在过惩罚方案中出现的病态条件问题，我们引入了一个复杂的分裂方法，将不连续解部分的方程组与连续解部分的方程组分开，从而得到行为良好的子问题。 我们证明了离散解的存在性和最优误差估计，这些结果通过数值验证得到了确认。 显示英文摘要

摘要： We propose a locally conservative enriched Galerkin scheme that respects the discrete maximum principle of an elliptic problem. To this end, we use a substantial over-penalization of the discrete solution's jumps to obtain optimal convergence. To avoid the ill-conditioning issues that arise in over-penalized schemes, we introduce an involved splitting approach that separates the system of equations for the discontinuous solution part from the system of equations for the continuous solution part, yielding well-behaved subproblems. We prove the existence of discrete solutions and optimal error estimates, which are validated numerically.