Stability of 2D FDTD algorithms with local mesh refinement for Maxwell's equations

Generalized 2d Delaunay Mesh Refinement

Delaunay refinement is a popular mesh generation method which makes it possible to derive mathematical guarantees with respect to the quality of the elements. Traditional Delaunay refinement algorithms insert Steiner points in a small enumerable number (one or two) of specific positions inside circumscribed circles of poor quality triangles and on encroached segments. In this paper we prove tha...

Stability of Interfaces with Mesh Refinement

We study the stability of mesh refinement in space and time for several different interface equations and finite-difference approximations. First, we derive a root condition which implies stability for the initial-boundary value problem for this type of interface. From the root condition, we prove the stability of several interface equations using the maximum principle. In some cases, the final...

Domain Decomposition with Local Mesh Refinement

Local Mesh Refinement with the PCD Method

We propose some numerical tests for local mesh refinement using the PCD (piecewise constant distributions) method. The PCDmethod is a new discretization technique of boundary value problems. It represents the unknown distribution as well as its derivatives by piecewise constant distributions but on distinct meshes. With the PCDmethod, we can introduce a local mesh refinement without the use of ...

Mesh Refinement For Stabilized Convection Diffusion Equations

We derive a residual a posteriori error estimates for the subscales stabilization of convection diffusion equation. The estimator yields upper bound on the error which is global and lower bound that is local.