We consider the least-squares finite element method (lsfem) for systems of nonlinear ordinary differential equations, and establish an optimal error estimate this when piecewise linear elements are used. The main assumptions that vector field is sufficiently smooth local Lipschitz constant as well operator norm Jacobian matrix associated with nonlinearity small, restricted to a suitable neighbo...

This article studies the least-squares finite element method for the linearized, stationary Navier–Stokes equation based on the stress-velocity-pressure formulation in d dimensions (d = 2 or 3). The least-squares functional is simply defined as the sum of the squares of the L2 norm of the residuals. It is shown that the homogeneous least-squares functional is elliptic and continuous in the H(di...

Least squares kinetic upwind mesh-free (LSKUM) method has been the subject of research over twenty years in our research group. LSKUM method requires a cloud (W) of points or nodes and connectivity N(P 0 ) for every 0 P Î W . The connectivity of P0 is a set of neighbours 0 ( ) i P N P Î of P0. The cloud can be a simple cloud, Cartesian cloud or chimera cloud or can be obtained rapidly using adv...

X. Cui Department of Informatics, School of Multidisciplinary Sciences, The Graduate University for Advanced Studies (Sokendai), 2-1-2, Hitotsubashi, Chiyoda-ku, Tokyo, Japan, 101-8430 K. Hayami Principles of Informatics Research Division, National Institute of Informatics, 2-1-2, Hitotsubashi, Chiyodaku, Tokyo, Japan, 101-8430 J. Yin Department of Mathematics, Tongji University, Shanghai, P.R....

where L = (Lij)m×n is a block m×n matrix differential operator of at most first order, B = (Bij)l×n is a block l × n matrix operator, U = (Ui)n×1 is unknown, F = (Fi)m×1 is a given block vector-valued function defined in Ω, G = (Gi)l×1 is a given block vector-valued function defined on ∂Ω. Assume that first-order system (1.1) has a unique solution U . Boundary conditions in a least-squares form...