An abstract framework for parabolic PDEs on evolving spaces
We present an abstract framework for treating the theory of well-posedness of solutions to
abstract parabolic partial di¤ erential equations on evolving Hilbert spaces. This theory is …
abstract parabolic partial di¤ erential equations on evolving Hilbert spaces. This theory is …
A unified theory for continuous-in-time evolving finite element space approximations to partial differential equations in evolving domains
CM Elliott, T Ranner - IMA Journal of Numerical Analysis, 2021 - academic.oup.com
We develop a unified theory for continuous-in-time finite element discretizations of partial
differential equations posed in evolving domains, including the consideration of equations …
differential equations posed in evolving domains, including the consideration of equations …
[HTML][HTML] A velocity-based moving mesh virtual element method
We present a velocity-based moving mesh virtual element method for the numerical solution
of PDEs involving boundaries which are free to move. The virtual element method is used for …
of PDEs involving boundaries which are free to move. The virtual element method is used for …
High-order finite element methods for moving boundary problems with prescribed boundary evolution
We introduce a framework for the design of finite element methods for two-dimensional
moving boundary problems with prescribed boundary evolution that have arbitrarily high …
moving boundary problems with prescribed boundary evolution that have arbitrarily high …
On some linear parabolic PDEs on moving hypersurfaces
We consider existence and uniqueness for several examples of linear parabolic equations
formulated on moving hypersurfaces. Specifically, we study in turn a surface heat equation …
formulated on moving hypersurfaces. Specifically, we study in turn a surface heat equation …
An energy stable one-field monolithic arbitrary Lagrangian–Eulerian formulation for fluid–structure interaction
In this article we present a one-field monolithic finite element method in the Arbitrary
Lagrangian–Eulerian (ALE) formulation for Fluid–Structure Interaction (FSI) problems. The …
Lagrangian–Eulerian (ALE) formulation for Fluid–Structure Interaction (FSI) problems. The …
Isoparametric Virtual Element Methods
We present two approaches to constructing isoparametric Virtual Element Methods of
arbitrary order for linear elliptic partial differential equations on general two-dimensional …
arbitrary order for linear elliptic partial differential equations on general two-dimensional …
Time-discrete higher order ALE formulations: A priori error analysis
We derive optimal a priori error estimates for discontinuous Galerkin (dG) time discrete
schemes of any order applied to an advection–diffusion model defined on moving domains …
schemes of any order applied to an advection–diffusion model defined on moving domains …
[图书][B] Computational methods for complex liquid-fluid interfaces
This book highlights key computational challenges involved in the two-way coupling of
complex liquid-fluid interfaces. Including pivotal applications as examples, the text defines …
complex liquid-fluid interfaces. Including pivotal applications as examples, the text defines …
Partial differential equations with random input data: A perturbation approach
D Guignard - Archives of Computational Methods in Engineering, 2019 - Springer
We study the numerical approximation of partial differential equations with random input
data. Such problems arise when the uncertainty of the underlying system is taken into …
data. Such problems arise when the uncertainty of the underlying system is taken into …