Stabilization-free serendipity virtual element method for plane elasticity

Abstract: 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 $L^2$ norm and energy seminorm that match theoretical estimates as well as the convergence rates from higher order virtual element methods.