48 citations · 59 across the 5 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…