Adaptive Refinement Methods for Nonlinear Parabolic Partial Differential Equations.
RENSSELAER POLYTECHNIC INST TROY NY DEPT OF MATHEMATICAL SCIENCES
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This document considers two adaptive finite element techniques for parabolic partial differential equations PDEs that are based on using error estimates to control mesh refinement. One technique is a method of lines approach that uses a Galerkin method to discretize the PDEs in space and implicit multi-step integration in time. Spatial elements are added and deleted in regions of high and low error and are all advanced with the same sequence of varying time steps. The second technique is a local refinement method that uses Galerkin approximations in both space and time. Fine grids of space-time elements are added to coarser grids and the problem is recursively solved in regions of high error. Author
- Numerical Mathematics