This paper is devoted to a study of the numerical solution of the elastic-rigid obstacle problem by discontinuous Galerkin methods. A priori error estimates are established for numerous discontinuous Galerkin schemes, which are of optimal order for the linear element under appropriate solution regularity assumptions. The penalty method is applied to the discontinuous Galerkin approximation problems, and its convergence result is proved. Several numerical examples are reported on using linear elements and quadratic elements to solve the elastic-rigid obstacle problems, which show the effectiveness of the proposed method.
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