LC v-ST/FEM: a third-order accurate dissipation-controlled velocity-based space-time finite element method for solid dynamics and earthquake engineering problems

抄録

This paper presents details of a third-order accurate and unconditionally stable time-discontinuous Galerkin Space-Time Finite Element Method (ST/FEM) for solving solid-dynamics and earthquake engineering problems. This method is derived by employing the newly developed concept of displacement functions for satisfying the displacement-velocity relationships. The proposed method, which is designated as LC v-ST/FEM, is derived from the linear combination of displacement functions of single-field and two-field ST/FEMs. Consequently, LC v-ST/FEM has a user-defined parameter 0 ≤ α ≤1, which is introduced for controlling the high-frequency dissipation characteristics. From numerical analysis and solutions of benchmark problems, it is demonstrated that the proposed method is the third-order accurate in time, unconditionally stable, and contains negligible numerical dispersion error for all 0 ≤ α≤1. Moreover, for α ≠ 0, the method can attenuate the spurious high-frequency components from the velocity and displacement fields.