
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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A scalable and robust preconditioner for highorder FEM based on the fast diagonalization method
Pavarino proved that the additive Schwarz method with vertex patches and...
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Control of bifurcation structures using shape optimization
Many problems in engineering can be understood as controlling the bifurc...
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A new mixed finiteelement method for the biharmonic problem
Fourthorder differential equations play an important role in many appli...
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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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Code generation for productive portable scalable finite element simulation in Firedrake
Creating scalable, high performance PDEbased simulations requires a sui...
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Bifurcation analysis of twodimensional Rayleigh–Bénard convection using deflation
We perform a bifurcation analysis of the steady state solutions of Rayle...
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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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Irksome: Automating Runge–Kutta timestepping for finite element methods
While implicit Runge–Kutta methods possess high order accuracy and impor...
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Augmented saddle point formulation of the steadystate Stefan–Maxwell diffusion problem
We investigate structurepreserving finite element discretizations of th...
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Computing multiple solutions of topology optimization problems
Topology optimization problems often support multiple local minima due t...
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A Reynoldsrobust preconditioner for the Reynoldsrobust ScottVogelius discretization of the stationary incompressible NavierStokes equations
Augmented Lagrangian preconditioners have successfully yielded Reynolds...
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Augmented Lagrangian preconditioners for the OseenFrank model of cholesteric liquid crystals
We propose a robust and efficient augmented Lagrangiantype precondition...
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Robust multigrid methods for nearly incompressible elasticity using macro elements
We present a meshindependent and parameterrobust multigrid solver for ...
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PCPATCH: software for the topological construction of multigrid relaxation methods
Effective relaxation methods are necessary for good multigrid convergenc...
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A local Fourier analysis of additive Vanka relaxation for the Stokes equations
Multigrid methods are popular solution algorithms for many discretized P...
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Patrick E. Farrell
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