245 research outputs found
Improving Newton's method performance by parametrization: the case of Richards equation
The nonlinear systems obtained by discretizing degenerate parabolic equations
may be hard to solve, especially with Newton's method. In this paper, we apply
to Richards equation a strategy that consists in defining a new primary unknown
for the continuous equation in order to stabilize Newton's method by
parametrizing the graph linking the pressure and the saturation. The resulting
form of Richards equation is then discretized thanks to a monotone Finite
Volume scheme. We prove the well-posedness of the numerical scheme. Then we
show under appropriate non-degeneracy conditions on the parametrization that
Newton\^as method converges locally and quadratically. Finally, we provide
numerical evidences of the efficiency of our approach
Mini-Workshop: Numerical Analysis for Non-Smooth PDE-Constrained Optimal Control Problems
This mini-workshop brought together leading experts working on various aspects of numerical analysis for optimal control problems with nonsmoothness. Fifteen extended abstracts summarize the presentations at this mini-workshop
Challenges in Optimal Control of Nonlinear PDE-Systems
The workshop focussed on various aspects of optimal control problems for systems of nonlinear partial differential equations. In particular, discussions around keynote presentations in the areas of optimal control of nonlinear/non-smooth systems, optimal control of systems involving nonlocal operators, shape and topology optimization, feedback control and stabilization, sparse control, and associated numerical analysis as well as design and analysis of solution algorithms were promoted. Moreover, also aspects of control of fluid structure interaction problems as well as problems arising in the optimal control of quantum systems were considered
Geometric partial differential equations: Theory, numerics and applications
This workshop concentrated on partial differential equations involving stationary and evolving surfaces in which geometric quantities play a major role. Mutual interest in this emerging field stimulated the interaction between analysis, numerical solution, and applications
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