No abstract

No abstract

We investigate ecient asymptotically correct a posteriori error estimates for the numerical approximation of two-point boundary value problems for second order ordinary dierential equations by piecewise polynomial collocation methods. Our error indicators are based on the defect of the collocation solution with respect to an associated exact dierence scheme and backsolving using a cheap, low order nite-dierence scheme. We prove high asymptotical correctness of this error indicator and illustrate the theoretical analysis by numerical examples.

The node moving and multistage node enrichment adaptive refinement procedures are extended in mixed discrete least squares meshless (MDLSM) method for efficient analysis of elasticity problems. In the formulation of MDLSM method, mixed formulation is accepted to avoid second-order differentiation of shape functions and to obtain displacements and stresses simultaneously. In the refinement procedures, a robust error estimator based on the value of the least square residuals functional of the governing differential equations and its boundaries at nodal points is used which is inherently available from the MDLSM formulation and can efficiently identify the zones with higher numerical errors. The results are compared with the refinement procedures in the irreducible formulation of discrete least squares meshless (DLSM) method and show the accuracy and efficiency of the proposed procedures. Also, the comparison of the error norms and convergence rate show the fidelity of the proposed adaptive refinement procedures in the MDLSM method.

No abstract