Аннотация:The paper extends weighted essentially non-oscillatory (WENO) methods to three dimensional mixed-element unstructured meshes, comprising tetrahedral, hexahedral, prismaticand pyramidal elements. Numerical results illustrate the convergence rates and nonoscillatory properties of the schemes for various smooth and discontinuous solutions testcases and the compressible Euler equations on various types of grids. Schemes of up to fifthorder of spatial accuracy are considered.