Robust exponential convergence of $$hp$$ h p -FEM in balanced norms for singularly perturbed reaction-diffusion equations
نویسندگان
چکیده
منابع مشابه
Robust exponential convergence of hp-FEM for singularly perturbed reaction diffusion systems with multiple scales
We consider the approximation of a coupled system of two singularly perturbed reactiondiffusion equations, with the finite element method. The solution to such problems contains boundary layers which overlap and interact, and the numerical approximation must take this into account in order for the resulting scheme to converge uniformly with respect to the singular perturbation parameters. We pr...
متن کاملRobust exponential convergence of hp-FEM for singularly perturbed reaction diffusion systems with multiple scales
We consider a coupled system of two singularly perturbed reaction-diffusion equations in one dimension. Associated with the two singular perturbation parameters 0 < ε μ 1, are boundary layers of length scales O(ε) and O(μ). We propose and analyze an hp finite element scheme which includes elements of size O(εp) and O(μp) near the boundary, where p is the degree of the approximating polynomials....
متن کاملHp Fem for Reaction-diiusion Equations I: Robust Exponential Convergence Seminar F Ur Angewandte Mathematik Eidgenn Ossische Technische Hochschule Ch-8092 Z Urich Switzerland Hp Fem for Reaction-diiusion Equations I: Robust Exponential Convergence
A singularly perturbed reaction-diiusion equation in two dimensions is considered. We assume analyticity of the input data, i.e., the boundary of the domain is an analytic curve and the right hand side is analytic. We show that the hp version of the nite element method leads to robust exponential convergence provided that one layer of needle elements of width O(p") is inserted near the domain b...
متن کاملAn hp finite element method for singularly perturbed systems of reaction- diffusion equations
We consider the approximation of a coupled system of two singularly perturbed reaction-diffusion equations by the finite element method. The solution to such problems contains boundary layers which overlap and interact, and the numerical approximation must take this into account in order for the resulting scheme to converge uniformly with respect to the singular perturbation parameters. We pres...
متن کاملThe hp finite element method for singularly perturbed systems of reaction-diffusion equations
We consider the approximation of a coupled system of two singularly perturbed reaction-diffusion equations by the finite element method. The solution to such problems contains boundary layers which overlap and interact, and the numerical approximation must take this into account in order for the resulting scheme to converge uniformly with respect to the singular perturbation parameters. We pres...
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: Calcolo
سال: 2015
ISSN: 0008-0624,1126-5434
DOI: 10.1007/s10092-015-0139-y