On the local discontinuous Galerkin method for linear elasticity
Summary: Following \textit{P. Castillo} et al. [SIAM J. Numer. Anal. 38, No. 5, 1676--1706 (2000; Zbl 0987.65111)] and \textit{B. Cockburn} [ZAMM, Z. Angew. Math. Mech. 83, No. 11, 731--754 (2003; Zbl 1036.65079)], a general framework of constructing discontinuous Galerkin (DG) methods is developed for solving the linear elasticity problem. The numerical traces are determined in view of a discrete stability identity, leading to a class of stable DG methods. A particular method, called the LDG method for linear elasticity, is studied in depth, which can be viewed as an extension of the LDG method discussed by Castillo et al. [loc. cit.] and Cockburn [loc. cit.]. The error bounds in \(L^{2}\)-norm, \(H^{1}\)-norm, and a certain broken energy norm are obtained. Some numerical results are provided to confirm the convergence theory established.
scientific article; zbMATH DE number 5793793
scientific article