Stabilization-free serendipity virtual element method for plane elasticity

We present a higher order stabilization-free virtual element method applied to plane elasticity problems. We utilize a serendipity approach to reduce the total number of degrees of freedom from the corresponding high-order approximations. The well-posedness of the problem is numerically studied via an eigenanalysis. The method is then applied to several benchmark problems from linear elasticity and we show that the method delivers optimal convergence rates in L2 norm and energy seminorm that match theoretical estimates as well as the convergence rates from higher order virtual element methods. (c) 2022 Elsevier B.V. All rights reserved.

Automated summary

We present a higher order stabilization-free virtual element method for plane elasticity problems, which reduces the degrees of freedom by utilizing a serendipity approach. The well-posedness of the problem is studied numerically via eigenanalysis. The method is then applied to benchmark problems in linear elasticity, showing optimal convergence rates in L2 norm and energy seminorm matching theoretical estimates and higher order virtual element methods.