Convergence and quasi-optimal cost of adaptive algorithms for nonlinear operators including iterative linearization and algebraic solver
A Haberl, D Praetorius, S Schimanko… - Numerische Mathematik, 2021 - Springer
We consider a second-order elliptic boundary value problem with strongly monotone and
Lipschitz-continuous nonlinearity. We design and study its adaptive numerical …
Lipschitz-continuous nonlinearity. We design and study its adaptive numerical …
Uniqueness of discrete solutions of nonmonotone PDEs without a globally fine mesh condition
Uniqueness of the finite element solution for nonmonotone quasilinear problems of elliptic
type is established in one and two dimensions. In each case, we prove a comparison …
type is established in one and two dimensions. In each case, we prove a comparison …
An Improved Method for Solving Quasi-linear Convection Diffusion Problems on a Coarse Mesh
S Pollock - SIAM Journal on Scientific Computing, 2016 - SIAM
A method is developed for solving quasi-linear convection diffusion problems starting on a
coarse mesh where the data and solution-dependent coefficients are unresolved, the …
coarse mesh where the data and solution-dependent coefficients are unresolved, the …
Discrete comparison principles for quasilinear elliptic PDE
Abstract Comparison principles are developed for piecewise linear finite element
approximations of quasilinear elliptic partial differential equations. We consider the analysis …
approximations of quasilinear elliptic partial differential equations. We consider the analysis …
Pseudo-time regularization for PDE with solution-dependent diffusion
S Pollock - arXiv preprint arXiv:1611.04054, 2016 - arxiv.org
This work unifies pseudo-time and inexact regularization techniques for nonmonotone
classes of partial differential equations, into a regularized pseudo-time framework …
classes of partial differential equations, into a regularized pseudo-time framework …