Related Experiment Video
Updated: Aug 14, 2025

Spatial Multiobjective Optimization of Agricultural Conservation Practices using a SWAT Model and an Evolutionary Algorithm
Published on: December 9, 2012
Goal-oriented adaptive finite element methods with optimal computational complexity
Roland Becker1, Gregor Gantner2, Michael Innerberger3
1IPRA-LMAP, Université de Pau et des Pays de l'Adour, Avenue de l'Université BP 1155, 64013 PAU Cedex, France.
Abstract:
We consider a linear symmetric and elliptic PDE and a linear goal functional. We design and analyze a goal-oriented adaptive finite element method, which steers the adaptive mesh-refinement as well as the approximate solution of the arising linear systems by means of a contractive iterative solver like the optimally preconditioned conjugate gradient method or geometric multigrid. We prove linear convergence of the proposed adaptive algorithm with optimal algebraic rates. Unlike prior work, we do not only consider rates with respect to the number of degrees of freedom but even prove optimal complexity, i.e., optimal convergence rates with respect to the total computational cost.
More Related Videos
Related Concept Videos
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
Fast Decoupled and DC Powerflow
Ampere-Maxwell's Law: Problem-Solving
To solve the problem, we can use the equations from the analysis of an RC circuit and Maxwell's version of Ampère's law.
For the first part of...
Typical Model Studies
Unsymmetric Loading of Thin-Walled Members: Problem Solving
To compute the shear forces, find the shear flow at a specific distance from the endpoint using the vertical shear and the moment of inertia values. The total shear force on the flange is calculated by integrating the shear flow from one end of the flange to the other.
Next, calculate the moments of...
Area Computation by the Alternative Coordinate Method

