We present a reduced basis method for parametrized linear elliptic partial differential equations (PDEs) in least-squares finite element framework. A rigorous and reliable error estimate is developed, shown to bound the with respect exact solution of PDE, contrast estimates that measure finite-dimensional (high-fidelity) approximation. It first-order formulation key ingredient. The demonstrated...

The standard approaches to solving overdetermined linear systems Ax ≈ b construct minimal corrections to the vector b and/or the matrix A such that the corrected system is compatible. In ordinary least squares (LS) the correction is restricted to b, while in data least squares (DLS) it is restricted to A. In scaled total least squares (Scaled TLS) [15], corrections to both b and A are allowed, ...

vii List of Figures x List of Tables xi I Direct Minimization of the Equation Residuals 1

boundary integral equations (bie) are reformulations of boundary value problems for partial differential equations. there is a plethora of research on numerical methods for all types of these equations such as solving by discretization which includes numerical integration. in this paper, the neumann problem is reformulated to a bie, and then moving least squares as a meshless method is describe...