Multi-Adaptive Galerkin Methods for ODEs II: implementation and Applications
نویسندگان
چکیده
منابع مشابه
Multi-Adaptive Galerkin Methods for ODEs II: implementation and Applications
Continuing the discussion of the multi-adaptive Galerkin methods mcG(q) and mdG(q) presented in [A. Logg, SIAM J. Sci. Comput., 24 (2003), pp. 1879–1902], we present adaptive algorithms for global error control, iterative solution methods for the discrete equations, features of the implementation Tanganyika, and computational results for a variety of ODEs. Examples include the Lorenz system, th...
متن کاملMulti-Adaptive Galerkin Methods for ODEs I
We present multi-adaptive versions of the standard continuous and discontinuous Galerkin methods for ODEs. Taking adaptivity one step further, we allow for individual timesteps, order and quadrature, so that in particular each individual component has its own time-step sequence. This paper contains a description of the methods, an analysis of their basic properties, and a posteriori error analy...
متن کاملMulti-adaptive Galerkin methods for ODEs V: Stiff problems
We develop the methodology of multi-adaptive time-stepping for stiff problems. The new algorithm is based on adaptively stabilized fixed point iteration on time slabs and a new method for the recursive construction of time slabs. Numerical examples are given for a series of well-known stiff and non-stiff test problems.
متن کاملAdaptive Fourier-Galerkin methods
We study the performance of adaptive Fourier-Galerkin methods in a periodic box in R d with dimension d ≥ 1. These methods offer unlimited approximation power only restricted by solution and data regularity. They are of intrinsic interest but are also a first step towards understanding adaptivity for the hp-FEM. We examine two nonlinear approximation classes, one classical corresponding to alge...
متن کاملAdaptive spacetime meshing for discontinuous Galerkin methods
Spacetime-discontinuous Galerkin (SDG) finite element methods are used to solve hyperbolic spacetime partial differential equations (PDEs) to accurately model wave propagation phenomena arising in important applications in science and engineering. Tent Pitcher is a specialized algorithm, invented by Üngör and Sheffer [2000], and extended by Erickson et al. [2005], to construct an unstructured s...
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: SIAM Journal on Scientific Computing
سال: 2004
ISSN: 1064-8275,1095-7197
DOI: 10.1137/s1064827501389734