Elliptic operators with discontinuous coefficients in meshfree GFDM

Abstract In phase change simulations, material properties such as density, viscosity, or thermal conductivity may exhibit jump discontinuities, possibly of several orders magnitude. These discontinuities represent interfaces between the phases, and they emerge naturally during simulation; thus, their exact location is generally unknown a priori. Our goal to simulate processes with meshfree generalized finite difference method in monolithic model without distinguishing different phases. There, mentioned above appear coefficients inside elliptic operators divergence form jumps must be treated adequately by numerical method. We present for discretizing discontinuous need domain decomposition tracking interfaces. facilitates construction diagonally dominant diffusion that lead M‐matrices discrete Poisson's equation, satisfy maximum principle. demonstrate applicability new case smooth diffusivity diffusivity. show first‐order accurate problems provides second‐order fourth‐order convergence continuous coefficients.