The problem of solution transfer between meshes arises frequently in computational physics, e.g. in Lagrangian methods where remeshing occurs. The interpolation process must be conservative, i.e. it must conserve physical properties, such as mass. We extend previous works -- which described the solution transfer process for straight sided unstructured meshes -- by considering high-order isoparametric meshes with curved elements. To facilitate solution transfer, we numerically integrate the product of shape functions via Green's theorem along the boundary of the intersection of two curved elements. We perform a numerical experiment and confirm the expected accuracy by transferring test fields across two families of meshes.

翻译：在计算物理学中，网格间的解传递问题频繁出现，例如在发生重网格划分的拉格朗日方法中。该插值过程必须是守恒的，即必须守恒物理属性（如质量）。本文通过考虑包含弯曲单元的高阶等参网格，扩展了先前针对直边非结构网格描述解传递过程的工作。为促进解传递，我们通过格林定理沿两个弯曲单元交集的边界，对形函数的乘积进行数值积分。我们进行了一项数值实验，通过在两个网格族之间传递测试场，确认了预期的精度。