Meshes and Geometry

Where the mesh has to be fine, and how to build it: a posteriori error estimation and adaptive refinement, and conformal maps that carry disk meshes to other domains.

Reading order.

1. Error estimation: A Posteriori Error Estimation and Adaptive Meshing, with the Residual Estimator for the Conductivity Equation, the Zienkiewicz-Zhu Estimator and Goal-Oriented Error Estimation for the measured quantities.
2. Refinement: Dörfler Marking, Hanging Nodes on quadrilaterals, Newest Vertex Bisection on triangles, and Coarsening of Bisection Meshes.
3. In EIT: Adaptive Meshing in EIT.
4. Geometry: Numerical Conformal Mapping, based on the Conformal Invariance of the Conductivity Equation.

Related. Fast solvers for the mapped meshes: Linear Solvers. Transferring conductivities between meshes: L2 Projection.

References

1. R. Verfürth (2013). A Posteriori Error Estimation Techniques for Finite Element Methods. Oxford University Press. doi:10.1093/acprof:oso/9780199679423.001.0001