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Topics in adaptive computational methods for differential equations
Claes Johnson,Johan Hoffman,Anders Logg +2 more
- pp 107-126
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This work discusses two topics of adaptive computational methods for differential equations: (i) individual time-stepping and (ii) subgrid modeling, and presents some applications including the computability of sub grid modeling.Abstract:
We discuss two topics of adaptive computational methods for differential equations: (i) individual time-stepping and (ii) subgrid modeling, and we present some applications including the computability and predictability of the Solar Sys- tem and aspects of subgrid modeling in convection-diffusion-reaction systems.read more
Citations
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Journal ArticleDOI
Stochastic finite element methods for partial differential equations with random input data
TL;DR: Several approaches to quantification of probabilistic uncertainties in the outputs of physical, biological, and social systems governed by partial differential equations with random inputs require, in practice, the discretization of those equations, including intrusive approaches such as stochastic Galerkin methods and non-intrusive approaches.
Journal ArticleDOI
An Adaptive Hybrid FEM/FDM Method for an Inverse Scattering Problem in Scanning Acoustic Microscopy
Larisa Beilina,Christian Clason +1 more
TL;DR: This work applies an adaptive hybrid FEM/FDM method to an inverse scattering problem for the time-dependent acoustic wave equation, where one seeks to reconstruct an unknown sound velocity c(x) from a single measurement of wave-reflection data on a small part of the boundary.
Journal ArticleDOI
Adaptive Finite Element Method for a coefficient inverse problem for the Maxwell's system
TL;DR: In this paper, the authors considered a coefficient inverse problem for the complete time dependent Maxwell's system in 3-D. The key idea is to use the adaptive finite element method for the solution.
Journal ArticleDOI
Nonlinear Galerkin methods for the model reduction of nonlinear dynamical systems
Hermann G. Matthies,Marcus Meyer +1 more
TL;DR: In this paper, the nonlinear Galerkin method is applied to the finite element model of a wind-turbine, where both the mechanical and the aerodynamical degrees of freedom can be considered for model reduction.
Journal Article
Adaptive Hybrid Finite Element/Difference method for Maxwell's equations
Larisa Beilina,Marcus J. Grote +1 more
TL;DR: A priori error estimate in finite element method is derived and numerical examples where the rate of convergence of the hybrid method is indicated, concluding that the hybrid approach may be an important tool to reduce the execution time and memory requirements for large scale computations.
References
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Journal ArticleDOI
Stochastic finite element methods for partial differential equations with random input data
TL;DR: Several approaches to quantification of probabilistic uncertainties in the outputs of physical, biological, and social systems governed by partial differential equations with random inputs require, in practice, the discretization of those equations, including intrusive approaches such as stochastic Galerkin methods and non-intrusive approaches.
Journal ArticleDOI
An Adaptive Hybrid FEM/FDM Method for an Inverse Scattering Problem in Scanning Acoustic Microscopy
Larisa Beilina,Christian Clason +1 more
TL;DR: This work applies an adaptive hybrid FEM/FDM method to an inverse scattering problem for the time-dependent acoustic wave equation, where one seeks to reconstruct an unknown sound velocity c(x) from a single measurement of wave-reflection data on a small part of the boundary.
Journal ArticleDOI
Adaptive Finite Element Method for a coefficient inverse problem for the Maxwell's system
TL;DR: In this paper, the authors considered a coefficient inverse problem for the complete time dependent Maxwell's system in 3-D. The key idea is to use the adaptive finite element method for the solution.
DissertationDOI
Reduktionsmethoden zur Simulation des aeroelastischen Verhaltens von Windkraftanlagen
TL;DR: In this paper, a mathematical model for simulation of aeroelastischen Wechselwirkungen bei windkraftanlagen is presented, in which Rotorblatter and Turm are modelliert mittels a geometrisch nichtlinearen Balkentheorie.
Nonlinear Galerkin Methods for the Model Reduction of Nonlinear Dynamical Systems: Revised and expanded version of a contribution to the EUROMECH Coloquium 427, ENS Cachan France, September 2001
TL;DR: In this paper, the nonlinear Galerkin method is applied to the finite element model of a windturbine, where both the mechanical and the aerodynamical degrees of freedom can be considered for model reduction.