MLS (moving least square)-based finite elements for three-dimensional nonmatching meshes and adaptive mesh refinement

With the aid of moving least square (MLS) approximation, a new class of three-dimensional finite elements are proposed for treating nonmatching meshes and adaptive mesh refinement, for which the existing finite elements are hardly efficient. With a special choice of the weight-function supports and the base functions, the method results in useful elements with the polynomial shape function, for which the C1 continuity breaks down on the boundaries between the neighboring subdomains comprising one element. The effectiveness of the new elements in handling the discontinuities due to nonmatching interfaces and automatic mesh refinement is demonstrated via three-dimensional examples.