I describe an adaptive h-reenement method for solving reaction-diiusion systems in three space dimensions on hexahedral grids. These grids typically have irregular (hanging) nodes. Solutions are calculated using Galerkin's method with a piecewise trilinear basis in space and a BDF code in time. New a posteriori error indicators based on interpolation error estimates for irregular grids are used...

A block lower-upper symmetric Gauss-Seidel (BLU-SGS) implicit dual time-stepping method is developed for moving body problems with hybrid dynamic grids. To simulate flows over complex configurations, a hybrid grid method is adopted in this paper. Body-fitted quadrilateral (quad) grids are generated first near solid bodies. An adaptive Cartesian mesh is then generated to cover the entire computa...

A cell by cell adaptive mesh technique is described and implemented to solve the Euler equations. The adaptive mesh scheme builds upon a staggered grid Lagrangian code similar to the AWE code CORVUS. The mesh is automatically refined in a cell by cell manner using a solution gradient refinement criteria. The method has the automatic response of adaptive mesh refinement but without storing and s...

Sparse grids, as studied by Zenger and Griebel in the last 10 years have been very successful in the solution of partial differential equations, integral equations and classification problems. Adaptive sparse grid functions are elements of a function space lattice. It is seen that such lattices allow the generalisation of sparse grid techniques to the fitting of very high-dimensional functions ...