# Adaptive Finite Difference Methods for Nonlinear Elliptic and Parabolic Partial Differential Equations with Free Boundaries

@article{Oberman2016AdaptiveFD, title={Adaptive Finite Difference Methods for Nonlinear Elliptic and Parabolic Partial Differential Equations with Free Boundaries}, author={Adam M. Oberman and I. Zwiers}, journal={Journal of Scientific Computing}, year={2016}, volume={68}, pages={231-251} }

Monotone finite difference methods provide stable convergent discretizations of a class of degenerate elliptic and parabolic partial differential equations (PDEs). These methods are best suited to regular rectangular grids, which leads to low accuracy near curved boundaries or singularities of solutions. In this article we combine monotone finite difference methods with an adaptive grid refinement technique to produce a PDE discretization and solver which is applied to a broad class of… CONTINUE READING

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