First-order System Least-squares Methods for Partial Differential Equations
نویسنده
چکیده
In recent years there has been lots of interest in the use of first-order system leastsquares method (FOSLS) for numerical approximations of elliptic partial differential equations, Stokes equations, elasticity and Navier-Stokes equations. In this paper we will provide a brief review of FOSLS around elliptic problems and Stokes equations. FOSLS is to find a minimization solution which minimizes least-squares functional defined by summing appropriate norms of residual equations :
منابع مشابه
A Boundary Meshless Method for Neumann Problem
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...
متن کاملLeast Squares Methods for Models Including Ordinary and Partial Differential Equations
This contribution gives a brief overview on nonlinear constrained least squares methods. The focus is on data fitting problems in which the models include ordinary or partial differential equations.
متن کاملSolving high-order partial differential equations in unbounded domains by means of double exponential second kind Chebyshev approximation
In this paper, a collocation method for solving high-order linear partial differential equations (PDEs) with variable coefficients under more general form of conditions is presented. This method is based on the approximation of the truncated double exponential second kind Chebyshev (ESC) series. The definition of the partial derivative is presented and derived as new operational matrices of der...
متن کاملProjection Multilevel Methods for Quasilinear Elliptic Partial Differential Equations: Theoretical Results
In a companion paper [8], we propose a new multilevel solver for two-dimensional elliptic systems of partial differential equations (PDEs) with nonlinearity of type u∂v. The approach is based on a multilevel projection method (PML [9]) applied to a first-order system least-squares (FOSLS) functional that allows us to treat the nonlinearity directly. While [8] focuses on computation, here we con...
متن کاملSolving the fractional integro-differential equations using fractional order Jacobi polynomials
In this paper, we are intend to present a numerical algorithm for computing approximate solution of linear and nonlinear Fredholm, Volterra and Fredholm-Volterra integro-differential equations. The approximated solution is written in terms of fractional Jacobi polynomials. In this way, firstly we define Riemann-Liouville fractional operational matrix of fractional order Jacobi polynomials, the...
متن کامل