离散化
算法
趋同(经济学)
数学
粘弹性
应用数学
计算机科学
数学分析
物理
热力学
经济
经济增长
标识
DOI:10.1016/j.cma.2023.116452
摘要
We present a hybrid discontinuous Galerkin method for the velocity/stress formulation of Zener’s model in dynamic viscoelasticity. Our approach utilizes a spatial discretization that enforces strongly the symmetry of the stress tensor, and that allows for efficient handling of heterogeneous materials comprising both purely elastic and viscoelastic components. We provide an hp error analysis of the semidiscrete scheme, which yields quasi-optimal error estimates for the stress tensor and sub-optimal error estimates for the velocity field in the L2-norm. Next, we apply the Crank–Nicolson rule as a time-stepping scheme and analyze its primary convergence properties. Finally, we present the results of numerical experiments to validate our approach and confirm the theoretical rates of convergence.
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