TY - GEN
T1 - Corrected stabilized non-conforming nodal integration in meshfree methods
AU - Rüter, Marcus
AU - Hillman, Michael
AU - Chen, Jiun Shyan
PY - 2013
Y1 - 2013
N2 - A novel approach is presented to correct the error from numerical integration in Galerkin methods for meeting linear exactness. This approach is based on a Ritz projection of the integration error that allows a modified Galerkin discretization of the original weak form to be established in terms of assumed strains. The solution obtained by this method is the correction of the original Galerkin discretization obtained by the inaccurate numerical integration scheme. The proposed method is applied to elastic problems solved by the reproducing kernel particle method (RKPM) with first-order correction of numerical integration. In particular, stabilized non-conforming nodal integration (SNNI) is corrected using modified ansatz functions that fulfill the linear integration constraint and therefore conforming sub-domains are not needed for linear exactness. Illustrative numerical examples are also presented.
AB - A novel approach is presented to correct the error from numerical integration in Galerkin methods for meeting linear exactness. This approach is based on a Ritz projection of the integration error that allows a modified Galerkin discretization of the original weak form to be established in terms of assumed strains. The solution obtained by this method is the correction of the original Galerkin discretization obtained by the inaccurate numerical integration scheme. The proposed method is applied to elastic problems solved by the reproducing kernel particle method (RKPM) with first-order correction of numerical integration. In particular, stabilized non-conforming nodal integration (SNNI) is corrected using modified ansatz functions that fulfill the linear integration constraint and therefore conforming sub-domains are not needed for linear exactness. Illustrative numerical examples are also presented.
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U2 - 10.1007/978-3-642-32979-1_5
DO - 10.1007/978-3-642-32979-1_5
M3 - Conference contribution
AN - SCOPUS:84872290948
SN - 9783642329784
T3 - Lecture Notes in Computational Science and Engineering
SP - 75
EP - 92
BT - Meshfree Methods for Partial Differential Equations VI
T2 - 6th International Workshop on Meshfree Methods for Partial Differential Equations
Y2 - 4 October 2011 through 6 October 2011
ER -