A posteriori error estimates of higher-order finite elements for frictional contact problems

In this paper, a posteriori estimates are derived for higher-order finite element methods and frictional contact problems. The discretization is based on a mixed approach where the geometrical and frictional constraints are captured by Lagrange multipliers. The use of higher-order polynomials leads to a certain non-conformity in the discretization which requires special attention in the error analysis. As a main result an error estimation is proposed which consists of the dual norm of a residual plus some computable remainder terms. The residual is estimated by well-known a posteriori error estimates for variational equations. The remainder terms represent typical sources resulting from the non-conforming mixed discretization. Numerical experiments confirm the applicability of the a posteriori estimates to adaptive mesh refinements.

Highlight► A posteriori estimates are derived for frictional contact problems. ► Higher-order mixed finite elements are applied. ► The non-conformity of the discretization is considered in the error analysis. ► The applicability of the estimates to adaptive mesh refinements is discussed.