TY - JOUR

T1 - Solution of linear elastodynamics problems with space-time finite elements on structured and unstructured meshes

AU - Idesman, Alexander V.

PY - 2007/2/1

Y1 - 2007/2/1

N2 - A new implicit approach for the solution of linear elastodynamics problems on structured and unstructured meshes with space-time finite elements is suggested. New weak formulations are based on time continuous (TCG) and discontinuous (TDG) Galerkin methods. It was shown that for structured meshes, the new TCG method has a higher order of accuracy (by a factor of two) than that of the standard TCG method. At the same number of degrees of freedom the accuracy of the new TCG method is one order higher than the accuracy of the standard TDG method. The introduction of new weighting functions for the weak formulations of the TCG and TDG methods allows control of the high frequency behavior without degradation of accuracy of the methods. A variable number of elements in the time direction as well as a variable order of polynomial time approximations of finite elements for time slabs allows the implementation of a coupled space-time adaptive procedure using structured or unstructured meshes. Numerical examples for 1-D problems demonstrate the effectiveness of the technique.

AB - A new implicit approach for the solution of linear elastodynamics problems on structured and unstructured meshes with space-time finite elements is suggested. New weak formulations are based on time continuous (TCG) and discontinuous (TDG) Galerkin methods. It was shown that for structured meshes, the new TCG method has a higher order of accuracy (by a factor of two) than that of the standard TCG method. At the same number of degrees of freedom the accuracy of the new TCG method is one order higher than the accuracy of the standard TDG method. The introduction of new weighting functions for the weak formulations of the TCG and TDG methods allows control of the high frequency behavior without degradation of accuracy of the methods. A variable number of elements in the time direction as well as a variable order of polynomial time approximations of finite elements for time slabs allows the implementation of a coupled space-time adaptive procedure using structured or unstructured meshes. Numerical examples for 1-D problems demonstrate the effectiveness of the technique.

KW - High-order accurate methods

KW - Linear dynamics

KW - Space-time elements

UR - http://www.scopus.com/inward/record.url?scp=33845634391&partnerID=8YFLogxK

U2 - 10.1016/j.cma.2006.09.019

DO - 10.1016/j.cma.2006.09.019

M3 - Article

AN - SCOPUS:33845634391

VL - 196

SP - 1787

EP - 1815

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0045-7825

IS - 9-12

ER -