  In this paper we propose a novel numerical scheme for the
Canham-Helfrich-Evans bending energy based on a three-field lifting procedure
of the distributional shape operator to an auxiliary mean curvature field.
Together with its energetic conjugate scalar stress field as Lagrange
multiplier the resulting fourth order problem is circumvented and reduced to a
mixed saddle point problem involving only second order differential operators.
Further, we derive its analytical first variation (also called first shape
derivative), which is valid for arbitrary polynomial order, and discuss how the
arising shape derivatives can be computed automatically in the finite element
software NGSolve. We finish the paper with several numerical simulations
showing the pertinence of the proposed scheme and method.
