A Shishkin mesh for a singularly perturbed Riccati equation
نویسندگان
چکیده
منابع مشابه
Analysis of a Streamline-Diffusion Finite Element Method on Bakhvalov-Shishkin Mesh for Singularly Perturbed Problem
Abstract. In this paper, a bilinear Streamline-Diffusion finite element method on Bakhvalov-Shishkin mesh for singularly perturbed convection – diffusion problem is analyzed. The method is shown to be convergent uniformly in the perturbation parameter ǫ provided only that ǫ ≤ N. An O(N(lnN)) convergent rate in a discrete streamline-diffusion norm is established under certain regularity assumpti...
متن کاملConvergence of the Multiplicative Schwarz Method for Singularly Perturbed Convection-diffusion Problems Discretized on a Shishkin Mesh∗
We analyze the convergence of the multiplicative Schwarz method applied to nonsymmetric linear algebraic systems obtained from discretizations of one-dimensional singularly perturbed convection-diffusion equations by upwind and central finite differences on a Shishkin mesh. Using the algebraic structure of the Schwarz iteration matrices we derive bounds on the infinity norm of the error that ar...
متن کاملUniformly Convergent 3-tgfem Vs Lsfem for Singularly Perturbed Convection-diffusion Problems on a Shishkin Based Logarithmic Mesh
In the present work, three-step Taylor Galerkin finite element method(3TGFEM) and least-squares finite element method(LSFEM) have been discussed for solving parabolic singularly perturbed problems. For singularly perturbed problems, a small parameter called singular perturbation parameter is multiplied with the highest order derivative term. As this singular perturbation parameter approaches to...
متن کاملA revised Kleinman algorithm to solve algebraic Riccati equation of singularly perturbed systems
In this paper, we show that the Kleinman algorithm can be used well to solve the algebraic Riccati equation (ARE) of singularly perturbed systems, where the quadratic term of the ARE may be inde1nite. The quadratic convergence property of the Kleinman algorithm is proved by using the Newton–Kantorovich theorem when the initial condition is chosen appropriately. In addition, the numerical method...
متن کاملUniform Approximation of Singularly Perturbed Reaction-Diffusion Problems by the Finite Element Method on a Shishkin Mesh
We consider the numerical approximation of singularly perturbed reaction-diffusion problems over twodimensional domains with smooth boundary. Using the h version of the finite element method over appropriately designed piecewise uniform (Shishkin) meshes, we are able to uniformly approximate the solution at a quasi-optimal rate. The results of numerical computations showing agreement with the a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2005
ISSN: 0377-0427
DOI: 10.1016/j.cam.2004.12.018