The hierarchical basis extrapolation method
SIAM Journal on Scientific and Statistical Computing - Special issue on iterative methods in numerical linear algebra
Numerics and hydrodynamic stability: toward error control in computational fluid dynamics
SIAM Journal on Numerical Analysis
The 4-triangles longest-side partition of triangles and linear refinement algorithms
Mathematics of Computation
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
SIAM Journal on Scientific Computing
An Adaptive Finite Element Method for Unsteady Convection-Dominated Flows with Stiff Source Terms
SIAM Journal on Scientific Computing
The Quadtree and Related Hierarchical Data Structures
ACM Computing Surveys (CSUR)
Adaptive Galerkin finite element methods for partial differential equations
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
A moving mesh finite element method for the two-dimensional Stefan problems
Journal of Computational Physics
Circuit, Device, and Process Simulation: Mathematical and Numerical Aspects
Circuit, Device, and Process Simulation: Mathematical and Numerical Aspects
Adaptive Finite Element Methods for Optimal Control of Partial Differential Equations: Basic Concept
SIAM Journal on Control and Optimization
SIAM Journal on Numerical Analysis
Application of adaptive mesh refinement method to complex flows in clean rooms
International Journal of Computational Fluid Dynamics
Mesh algorithms for PDE with Sieve I: Mesh distribution
Scientific Programming
Neural, Parallel & Scientific Computations
Hi-index | 0.00 |
We consider the use of adaptive mesh strategies for solution of problems exhibiting boundary and interior layer solutions. As the presence of these layer structures suggests, reliable and accurate solution of this class of problems using finite difference, finite volume or finite element schemes requires grading the mesh into the layers and due attention to the associated algorithms. When the nature and structure of the layer is known, mesh grading can be achieved during the grid generation by specifying an appropriate grading function. However, in many applications the location and nature of the layer behavior is not known in advance. Consequently, adaptive mesh techniques that employ feedback from intermediate grid solutions are an appealing approach. In this paper, we provide a brief overview of the main adaptive grid strategies in the context of problems with layers. Associated error indicators that guide the refinement feedback control/grid optimization process are also covered and there is a brief commentary on the supporting data structure requirements. Some current issues concerning the use of stabilization in conjunction with adaptive mesh refinement (AMR), the question of "pollution effects" in computation of local error indicators, the influence of nonlinearities and the design of meshes for targeted optimization of specific quantities are considered. The application of AMR for layer problems is illustrated by means of case studies from semiconductor device transport (drift diffusion), nonlinear reaction-diffusion, layers due to surface capillary effects, and shockwaves in compressible gas dynamics.