𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A two-grid method for mixed finite-element solution of reaction-diffusion equations

✍ Scribed by Li Wu; Myron B. Allen III

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
392 KB
Volume
15
Category
Article
ISSN
0749-159X

No coin nor oath required. For personal study only.

✦ Synopsis

We present a scheme for solving two-dimensional, nonlinear reaction-diffusion equations,

using a mixed finite-element method. To linearize the mixed-method equations, we use a two grid scheme that relegates all the Newton-like iterations to a grid H much coarser than the original one h , with no loss in order of accuracy so long as the mesh sizes obey H = O( √ h). The use of a multigrid-based solver for the indefinite linear systems that arise at each coarse-grid iteration, as well as for the similar system that arises on the fine grid, allows for even greater efficiency.

πŸ“œ SIMILAR VOLUMES

Two-grid methods for mixed finite-elemen
Two-grid methods for mixed finite-element solution of coupled reaction-diffusion systems
✍ Li Wu; Myron B. Allen πŸ“‚ Article πŸ“… 1999 πŸ› John Wiley and Sons 🌐 English βš– 423 KB πŸ‘ 1 views

We develop 2-grid schemes for solving nonlinear reaction-diffusion systems: where p = (p, q) is an unknown vector-valued function. The schemes use discretizations based on a mixed finite-element method. The 2-grid approach yields iterative procedures for solving the nonlinear discrete equations. Th

Mixed finite elements and Newton-type li
Mixed finite elements and Newton-type linearizations for the solution of Richards' equation
✍ Luca Bergamaschi; Mario Putti πŸ“‚ Article πŸ“… 1999 πŸ› John Wiley and Sons 🌐 English βš– 264 KB

We present the development of a two-dimensional Mixed-Hybrid Finite Element (MHFE) model for the solution of the non-linear equation of variably saturated ow in groundwater on unstructured triangular meshes. By this approach the Darcy velocity is approximated using lowest-order Raviart-Thomas (RT0)

Iterative solution of systems of equatio
Iterative solution of systems of equations in the dual reciprocity boundary element method for the diffusion equation
✍ V. Bulgakov; B. Ε arler; G. Kuhn πŸ“‚ Article πŸ“… 1998 πŸ› John Wiley and Sons 🌐 English βš– 233 KB πŸ‘ 1 views

In this paper the diffusion equation is solved in two-dimensional geometry by the dual reciprocity boundary element method (DRBEM). It is structured by fully implicit discretization over time and by weighting with the fundamental solution of the Laplace equation. The resulting domain integral of the