# Incremental unknowns for solving partial differential equations

@article{Chen1991IncrementalUF, title={Incremental unknowns for solving partial differential equations}, author={Min Chen and Roger Temam}, journal={Numerische Mathematik}, year={1991}, volume={59}, pages={255-271} }

SummaryIncremental unknowns have been proposed in [T] as a method to approximate fractal attractors by using finite difference approximations of evolution equations. In the case of linear elliptic problems, the utilization of incremental unknown methods provides a new way for solving such problems using several levels of discretization; the method is similar but different from the classical multigrid method.In this article we describe the application of incremental unknowns for solving Laplace… Expand

#### 72 Citations

Preconditioned Newton methods using incremental unknowns methods for the resolution of a steady-state Navier-Stokes-like problem

- Mathematics
- 1997

In a previous work, one of the authors has studied a numerical treatment (by fully implicit discretizations) of a two-dimensional Navier-Stokes-like problem and has proved existence and convergence… Expand

Incremental unknowns for solving nonlinear eigenvalue problems: New multiresolution methods

- Mathematics
- 1995

In this article, we present several numerical multilevel schemes for the solution of nonlinear eigenvalue problems. Using the Incremental Unknowns, we construct some generalization of the Marder and… Expand

NONLINEAR GALERKIN METHOD WITH MULTILEVEL INCREMENTAL UNKNOWNS

- Mathematics
- 1993

Multilevel methods are indispensable for the approximation of nonlinear evolution equations when complex physical phenomena involving the interaction of many scales are present (such as in, but… Expand

Solution of generalized Stokes problems using hierarchical methods and incremental unknowns

- Mathematics
- 1996

In this article, we present a nonstandard hierarchization of the MAC meshing associated with a second order finite difference discretization for the solution of generalized Stokes problems. Two… Expand

Nonlinear stability of reaction-diffusion equations using wavelet-like incremental unknowns

- Mathematics
- 2013

Incremental unknowns of different types were proposed as a means to develop numerical schemes in the context of finite difference discretizations. In this article, we present a novel wavelet-like… Expand

Solving the general elliptic equations with the incremental unknowns methods on floated grid

- Mathematics
- The 2nd International Conference on Information Science and Engineering
- 2010

Through numerical solutions of two-dimensional secondorder Dirichlet boundary-value, The discretization of the article is more simply than the classical grid. the incremental unknowns is linear… Expand

Preconditioning analysis of nonuniform incremental unknowns method for two dimensional elliptic problems

- Mathematics
- 2015

Abstract For the linear system obtained by discretizing two dimensional elliptic boundary value problems on nonuniform meshes, the condition number of the coefficient matrix preconditioned by… Expand

The matricial framework for the incremental unknowns method

- Mathematics
- 1993

The Incremental Unknowns Method has first been introduced in [7] to study the long time integration of dissipative evolution equations when finite-difference approximations of such equations are… Expand

Solution of generalized Stokes problems using hierarchical methods and Incremental Unknowns

- 2003

In this article, we present a nonstandard hierarchization of the MAC meshing associated with a second order finite difference discretization for the solution of generalized Stokes problems. Two… Expand

Incremental unknowns for solving the incompressible Navier—Stokes equations

- Mathematics
- 2000

Incremental unknowns, earlier designed for the long-term integration of dissipative evolutionary equations, are introduced here for the incompressible Navier–Stokes equations in primitive variables… Expand

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