  This paper develops an analogue (or counterpart) to discontinuous Galerkin
(DG) methods for approximating a general class of calculus of variations
problems. The proposed method, called the discontinuous Ritz (DR) method,
constructs a numerical solution by minimizing a discrete energy over DG
function spaces. The discrete energy includes standard penalization terms as
well as the DG finite element (DG-FE) numerical derivatives developed recently
by Feng, Lewis, and Neilan in [Feng2013]. It is proved that the proposed DR
method converges and that the DG-FE numerical derivatives exhibit a compactness
property which is desirable and crucial for applying the proposed DR method to
problems with more complex energy functionals. Numerical tests are provided on
the classical $p$-Laplace problem to gauge the performance of the proposed DR
method.
