Virtual Element Computation Of A Kind Of Glacier Model

Numerical simulation of glacier and ice sheet evolution is a subject of increasing interest,in part because the model may provide information for the estimation of global sea level change.Because of the complexity of glacier model itself,regional and boundary conditions,it is difficult for the conventional numerical methods to achieve good results when considering large-scale,high-resolution,time evolution simulation of real glaciers and ice sheets.Compared with the finite element method,the virtual element method,as a development of the finite element method,has lower requirements for the shape of the element,and can adapt to the complex boundary conditions and regions.A virtual element method(VEM)for solving the Stokes model of continental glaciers is presented in this paper,we solve the nonlinear equations by the Newton-Raphson iteration.The convergence of the method is analyzed theoretically by this article.For triangle,quadrilateral and pentagon mesh,the key matrix is calculated in detail.Numerical examples verify the correctness of the method in triangular and square subdivision,and good results are obtained in terms of velocity and pressure.