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### What simple methods are there for adaptively sampling a 2D function?

I have a two-dimensional function $f(x,y)$ whose values I would like to sample. The function is very expensive to compute and it has a complex shape, so I need to find a way to get the most ...
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### Is there a general-purpose library for structured grid adaptive mesh refinement?

Adaptive mesh refinement (AMR) is a common technique for dealing with the problem of widely varying spatial scales in the numerical solution of PDEs. What general-purpose libraries exist for AMR on ...
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### What are the basic principles behind generating a moving mesh?

I am interested in implementing an moving mesh for an advection-diffusion problem. Adaptive Moving Mesh Methods gives a good example of how to do this for Burger's equation in 1D using finite-...
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### Finite Element Method vs Extended Finite Element Method (FEM vs XFEM)

What are main differences between FEM and XFEM? When should we (not) use XFEM intead of FEM and vice versa? In other words, when I meet a new problem, how I can know to use which one of them?
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### What are the strategies for local Adaptive Mesh Refinement (local AMR) on unstructured meshes?

I am interested in local AMR on unstructured meshes. Currently, I'm working with the OpenFOAM library - it supports completely unstructured local AMR: cell refinement criteria determine a list of ...
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What are the "Pros and Cons" for these two methods of mesh-refinement? Both seem to be the prevalent methods. I can naturally imagine that global red refinement is comparatively easy to implement and ...
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### Adaptive mesh refinement with perfectly matched layers?

We have an adaptive mesh refinement (AMR) code for solving the elastic wave equation with frictional fault interfaces (based on Chombo for those that are interested). One of the things that we have ...
188 views

I am working on solving complex system of 2D PDEs governing the behaviour of plasma in a gas lamp during discharge. Recent tests have shown that because of steep gradients in temperature field and ...
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### Conforming mesh refinement for quads/hex elements

The context - I'm working with a spectral FE (higher order interpolation at GLL nodes) code on conforming hexahedral meshes, and our PI is interested in improving mesh quality, possibly with adaptive ...
133 views

### Convergence of adaptive finite elements with inexact solves

I'm working on some adaptive discontinuous Galerkin codes for time harmonic wave propagation, currently just Helmholtz, but will be branching out once I have a working prototype in this case. There ...