An adaptive multilevel local defect correction technique with application to combustion

Local Defect Correction Techniques Applied to a Combustion Problem

The standard local defect correction (LDC) method has been extended to include multilevel adaptive gridding, domain decomposition, and regridding. The domain decomposition algorithm provides a natural route for parallelization by employing many small tensor-product grids, rather than a single large unstructured grid. The algorithm is applied to a laminar Bunsen flame with one-step chemistry.

Local defect correction with slanting grids

The local defect correction (LDC) method is used to solve a convection-diffusion-reaction problem that contains a high activity region in a relatively small part of the domain. The improvement of the solution on a coarse grid is obtained by introducing a correction term computed from a local fine grid solution. This paper studies problems where the high activity region is covered with a rectang...

Adaptive Multilevel Methods with Local Smoothing

A multilevel method on adaptive meshes with hanging nodes is derived. Smoothing is restricted to the interior of the subdomains refined to the current level, thus has optimal computational complexity. Its convergence rates are the same as for the the non-adaptive version. We discuss the implementation in a general finite element code at the example of the deal.II library.

On Reducing sequences and an Application to Local Cohomology Modules

An adaptive combustion framework