What question did this study set out to answer?

To construct and mathematically prove the convergence of an adaptive finite element algorithm for solving Poisson's equation in two space dimensions.

June 1, 1996SIAM Journal on Numerical Analysis

A Convergent Adaptive Algorithm for Poisson’s Equation

View Full Paper

Ask AI

Bookmark

Authors

WDWilly DörflerKarlsruhe Institute of Technology

Discussion

Member takes

Implication

Theoretical analysis demonstrates constant-rate error reduction for adaptive linear elements in two-dimensional Poisson equations, indicating guaranteed convergence to prescribed tolerance bounds.

Key Points

To construct and mathematically prove the convergence of an adaptive finite element algorithm for solving Poisson's equation in two space dimensions.
Constructed an initial grid from a macro triangulation using a priori information.
Used a posteriori error estimators to iteratively generate a sequence of refined triangulations and approximate solutions for linear elements, with extensions to higher-order elements.
Proved that the approximation error, evaluated in the energy norm, decreases at a constant rate at each refinement step until a prescribed error threshold is reached.
Confirmed convergence behavior and algorithmic performance across two-dimensional domains through numerical experiments.

Cite This Study

Willy Dörfler (1996) studied this question.

synapsesocial.com/papers/69dc2373ea70a37eff955331 https://doi.org/10.1137/0733054

View Full Paper

Ask AI

Bookmark

Implication

Theoretical analysis demonstrates constant-rate error reduction for adaptive linear elements in two-dimensional Poisson equations, indicating guaranteed convergence to prescribed tolerance bounds.

A Convergent Adaptive Algorithm for Poisson’s Equation

Discussion

Member takes

Implication

Key Points

Cite This Study

A Convergent Adaptive Algorithm for Poisson’s Equation

Discussion

Member takes

Implication

Key Points

Cite This Study

Also Consider

Also Consider