Moving Mesh Methods for Problems with Blow-Up
نویسندگان
چکیده
منابع مشابه
Moving Mesh Methods for Problems with Blow-Up
In this paper we consider the numerical solution of PDEs with blow-up for which scaling invariance plays a natural role in describing the underlying solution structures. It is a challenging numerical problem to capture the qualitative behaviour in the blow-up region, and the use of nonuniform meshes is essential. We consider moving mesh methods for which the mesh is determined using so-called m...
متن کاملA Splitting Moving Mesh Method for 3-D Quenching and Blow-Up Problems
We present a splitting moving mesh method for multi-dimensional reaction-diffusion problems with nonlinear forcing terms over rectangular domains. The structure of the adaptive algorithm is an elegant combination of an operator splitting and one-dimensional moving mesh. It is motivated by the nature of splitting method, which splits a multi-dimensional problems into a few one-dimensional proble...
متن کاملMoving-Mesh Methods for One-Dimensional Hyperbolic Problems Using CLAWPACK
1. I N T R O D U C T I O N We study high-resolution finite-volume methods for the one-dimensional conservation law qt + f (q ) z = ~ (x ,q ) (1) on a moving grid, where the interface x~ between grid cells varies with time t~. Figure 1 shows a typical moving grid over one time step. We show how the wave-propagation algorithms developed in [1] and implemented in the CLAWPACK software [2] can be m...
متن کاملEvans function and blow-up methods in critical eigenvalue problems
Contact defects are one of several types of defects that arise generically in oscillatory media modelled by reaction-diffusion systems. An interesting property of these defects is that the asymptotic spatial wavenumber is approached only with algebraic order O(1/x) (the associated phase diverges logarithmically). The essential spectrum of the PDE linearization about a contact defect always has ...
متن کاملBlow-up for Parabolic and Hyperbolic Problems with Variable Exponents
In this paper we study the blow up problem for positive solutions of parabolic and hyperbolic problems with reaction terms of local and nonlocal type involving a variable exponent. We prove the existence of initial data such that the corresponding solutions blow up at a finite time.
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: 1996
ISSN: 1064-8275,1095-7197
DOI: 10.1137/s1064827594272025