48 citations · 100 across the 7 of their papers we have counts for
7 papers
An intrinsic finite element framework for scalar- and vector-valued partial differential equations on general manifolds
Tamara A. Tambyah, Alberto F. Martín, David Lee +1
We present an intrinsic finite element framework for the numerical approximation of scalar- and vector-valued partial differential equations on general manifolds described by atlas…
GridapGeosciences.jl: A Julia finite element package for partial differential equations on general manifolds
Tamara A. Tambyah, Alberto F. Martín, David Lee +1
We present GridapGeosciencesjl, a new parallel distributed-memory Julia package for the numerical approximation of partial differential equations on general manifolds. Our abstr…
Robust finite element methods and solvers for the Biot--Brinkman equations in vorticity form
Ruben Caraballo, Chansophea Wathanak In, Alberto F. Martín +1
In this paper, we propose a new formulation and a suitable finite element method for the steady coupling of viscous flow in deformable porous media using divergence-conforming filt…
Finite element interpolated neural networks for solving forward and inverse problems
Santiago Badia, Wei Li, Alberto F. Martín
We propose a general framework for solving forward and inverse problems constrained by partial differential equations, where we interpolate neural networks onto finite element spac…
A comparison of variational upwinding schemes for geophysical fluids, and their application to potential enstrophy conserving discretisations
David Lee, Alberto F. Martín, Christopher Bladwell +1
Methods for upwinding the potential vorticity in a compatible finite element discretisation of the rotating shallow water equations are studied. These include the well-known antici…
A robust and scalable unfitted adaptive finite element framework for nonlinear solid mechanics
Santiago Badia, Manuel Caicedo, Alberto F. Martín +1
In this work, we bridge standard adaptive mesh refinement and coarsening on scalable octree background meshes and robust unfitted finite element formulations for the automatic and…
The aggregated unfitted finite element method on parallel tree-based adaptive meshes
Santiago Badia, Alberto F. Martín, Eric Neiva +1
In this work, we present an adaptive unfitted finite element scheme that combines the aggregated finite element method with parallel adaptive mesh refinement. We introduce a novel…