In this article we consider the extension of the (L)SIAC-MRA enhancement procedure to nonuniform meshes. We demonstrate that error reduction can be obtained on perturbed quadrilateral and Delaunay meshes, and investigate the effect of limited resolution and its impact on the procedure for various function types. We show that utilizing mesh-based localized kernel scalings, which were shown to reduce approximation errors for LSIAC filters, improve the performance of the LSIAC-MRA enhancement procedure. Lastly, we demonstrate the usefulness of enhanced approximations generated by (L)SIAC-MRA in mesh adaptivity applications, and show that SIAC reconstruction can be used in identification of regions of high error in steady-state DG approximations.

翻译：本文研究将(L)SIAC-MRA增强方法推广至非均匀网格。我们证明该方案能在扰动四边形网格和Delaunay网格上实现误差降低，并探讨有限分辨率对不同类型函数处理过程的影响。研究表明，采用基于网格的局部核缩放（该方法已被证实可降低LSIAC滤波器的近似误差）能够提升LSIAC-MRA增强方法的性能。最后，我们展示了(L)SIAC-MRA生成的增强近似在网格自适应应用中的实用性，并证明SIAC重构可用于识别稳态DG近似中高误差区域。