Abstract

In this work we will present a method of virtual elements to approximate the solution of a polyharmonic problem (-Delta)������������ = ������. We will consider ������ + 1 auxiliary unknowns when ������ = 2 ������ + 1, and ������ auxiliary unknowns for ������ = 2 ������. In the first case (������ = 2 ������ + 1), we will solve ������ fourth order problems and a second order one. In the even case, only ������ fourth-order problems have to be solved. Virtual element conforming discretizations are written for each fourth -order problem in ������1, and a ������0-virtual element method is established for the second -order problem. We also carry out the error analysis for both cases. Finally, we report a series of numerical tests to verify the performance of numerical scheme.