SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page A2300-A2324, January 2020.
We devise and analyze a hybrid high-order (HHO) method to discretize unilateral and bilateral contact problems with Tresca friction in small strain elasticity. The nonlinear frictional contact conditions are enforced weakly by means of a consistent Nitsche technique with symmetric, incomplete, and skew-symmetric variants. The present HHO-Nitsche method supports polyhedral meshes and delivers optimal energy-error estimates for smooth solutions under some minimal thresholds on the penalty parameters for all the symmetry variants. An explicit tracking of the dependency of the penalty parameters on the material coefficients is carried out to identify the robustness of the method in the incompressible limit, showing the more advantageous properties of the skew-symmetric variant. Two- and three-dimensional numerical results, including comparisons to benchmarks from the literature and to solutions obtained with an industrial software, as well as a prototype for an industrial application, illustrate the theoretical results and reveal that in practice the method behaves in a robust manner for all the symmetry variants in Nitsche's formulation.

中文翻译：

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高应变离散和尼氏法相结合的混合高阶离散化

SIAM科学计算杂志，第42卷，第4期，第A2300-A2324页，2020年1月。
我们设计并分析一种混合高阶（HHO）方法，以离散小应变弹性中Tresca摩擦的单边和双边接触问题。非线性摩擦接触条件是通过具有对称，不完全和偏斜对称变体的一致Nitsche技术来弱执行的。目前的HHO-Nitsche方法支持多面体网格，并在所有对称变量的惩罚参数的某些最小阈值下，为平滑解提供了最佳的能量误差估计。对惩罚参数对材料系数的依赖性进行了明确的跟踪，以识别该方法在不可压缩极限内的稳健性，从而显示了偏斜对称变量的更有利的属性。二维和三维数值结果