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08/14/2023
A full approximation scheme multilevel method for nonlinear variational inequalities
We present the full approximation scheme constraint decomposition (FASCD...
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11/25/2022
Multigrid solvers for the de Rham complex with optimal complexity in polynomial degree
The Riesz maps of the L^2 de Rham complex frequently arise as subproblem...
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11/10/2022
Two conjectures on the Stokes complex in three dimensions on Freudenthal meshes
In recent years a great deal of attention has been paid to discretizatio...
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08/25/2022
Finite element methods for multicomponent convection-diffusion
We develop finite element methods for coupling the steady-state Onsager-...
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07/26/2022
Finite-element discretization of the smectic density equation
The density variation of smectic A liquid crystals is modelled by a four...
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02/23/2022
Structure-preserving and helicity-conserving finite element approximations and preconditioning for the Hall MHD equations
We develop structure-preserving finite element methods for the incompres...
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02/16/2022
Preconditioners for computing multiple solutions in three-dimensional fluid topology optimization
Topology optimization problems generally support multiple local minima, ...
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02/15/2022
Monolithic multigrid for implicit Runge-Kutta discretizations of incompressible fluid flow
Most research on preconditioners for time-dependent PDEs has focused on ...
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01/27/2022
Optimal control of Hopf bifurcations
We introduce a numerical technique for controlling the location and stab...
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11/10/2021
Numerical approximation of viscous contact problems applied to glacial sliding
Viscous contact problems describe the time evolution of fluid flows in c...
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10/13/2021
Variational and numerical analysis of a 𝐐-tensor model for smectic-A liquid crystals
We analyse an energy minimisation problem recently proposed for modellin...
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07/30/2021
On the finite element approximation of a semicoercive Stokes variational inequality arising in glaciology
Stokes variational inequalities arise in the formulation of glaciologica...
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07/30/2021
A scalable and robust preconditioner for high-order FEM based on the fast diagonalization method
Pavarino proved that the additive Schwarz method with vertex patches and...
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05/31/2021
Control of bifurcation structures using shape optimization
Many problems in engineering can be understood as controlling the bifurc...
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05/15/2021
A new mixed finite-element method for the biharmonic problem
Fourth-order differential equations play an important role in many appli...
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04/30/2021
An augmented Lagrangian preconditioner for the magnetohydrodynamics equations at high Reynolds and coupling numbers
The magnetohydrodynamics (MHD) equations are generally known to be diffi...
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04/16/2021
Code generation for productive portable scalable finite element simulation in Firedrake
Creating scalable, high performance PDE-based simulations requires a sui...
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02/21/2021
Bifurcation analysis of two-dimensional Rayleigh–Bénard convection using deflation
We perform a bifurcation analysis of the steady state solutions of Rayle...
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02/04/2021
Accurate numerical simulation of electrodiffusion and water movement in brain tissue
Mathematical modelling of ionic electrodiffusion and water movement is e...
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06/29/2020
Irksome: Automating Runge–Kutta time-stepping for finite element methods
While implicit Runge–Kutta methods possess high order accuracy and impor...
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06/05/2020
Augmented saddle point formulation of the steady-state Stefan–Maxwell diffusion problem
We investigate structure-preserving finite element discretizations of th...
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04/24/2020
Computing multiple solutions of topology optimization problems
Topology optimization problems often support multiple local minima due t...
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04/20/2020
A Reynolds-robust preconditioner for the Reynolds-robust Scott-Vogelius discretization of the stationary incompressible Navier-Stokes equations
Augmented Lagrangian preconditioners have successfully yielded Reynolds-...
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04/15/2020
Augmented Lagrangian preconditioners for the Oseen-Frank model of cholesteric liquid crystals
We propose a robust and efficient augmented Lagrangian-type precondition...
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02/06/2020
Robust multigrid methods for nearly incompressible elasticity using macro elements
We present a mesh-independent and parameter-robust multigrid solver for ...
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12/18/2019
PCPATCH: software for the topological construction of multigrid relaxation methods
Effective relaxation methods are necessary for good multigrid convergenc...
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08/26/2019