An efficient space-time adaptive wavelet Galerkin method for time-periodic parabolic partial differential equations
نویسندگان
چکیده
We introduce a multitree-based adaptive wavelet Galerkin algorithm for space-time discretized linear parabolic partial differential equations, focusing on time-periodic problems. It is shown that the method converges with the best possible rate in linear complexity and can be applied for a wide range of wavelet bases. We discuss the implementational challenges arising from the Petrov-Galerkin nature of the variational formulation and present numerical results for the heat and a convection-diffusion-reaction equation.
منابع مشابه
A three-step wavelet Galerkin method for parabolic and hyperbolic partial differential equations
A three-step wavelet Galerkin method based on Taylor series expansion in time is proposed. The scheme is third-order accurate in time and O(2−jp) accurate in space. Unlike Taylor–Galerkin methods, the present scheme does not contain any new higher-order derivatives which makes it suitable for solving non-linear problems. The compactly supported orthogonal wavelet bases D6 developed by Daubechie...
متن کاملOptimality of adaptive Galerkin methods for random parabolic partial differential equations
Galerkin discretizations of a class of parametric and random parabolic partial differential equations (PDEs) are considered. The parabolic PDEs are assumed to depend on a vector y = (y1, y2, ...) of possibly countably many parameters yj which are assumed to take values in [−1, 1]. Well-posedness of weak formulations of these parametric equation in suitable Bochner spaces is established. Adaptiv...
متن کاملExistence of solution and solving the integro-differential equations system by the multi-wavelet Petrov-Galerkin method
In this paper, we discuss about existence of solution for integro-differential system and then we solve it by using the Petrov-Galerkin method. In the Petrov-Galerkin method choosing the trial and test space is important, so we use Alpert multi-wavelet as basis functions for these spaces. Orthonormality is one of the properties of Alpert multi-wavelet which helps us to reduce computations in ...
متن کاملA Gauss Galerkin Finite-Difference Method for Singular Partial Differential Equations in Two Space Variables
A Gauss–Galerkin finite-difference method is proposed for the numerical solution of a class of linear, singular parabolic partial differential equations in two space dimensions. The method generalizes a Gauss– Galerkin method previously used for treating similar singular parabolic partial differential equations in one space dimension. Two test problems are studied and the numerical results are ...
متن کاملSpace-time radial basis function collocation method for one-dimensional advection-diffusion problem
The parabolic partial differential equation arises in many application of technologies. In this paper, we propose an approximate method for solution of the heat and advection-diffusion equations using Laguerre-Gaussians radial basis functions (LG-RBFs). The results of numerical experiments are compared with the other radial basis functions and the results of other schemes to confirm the validit...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Math. Comput.
دوره 85 شماره
صفحات -
تاریخ انتشار 2016