4 papers
A natural language framework for non-conforming hybrid polytopal methods in Gridap.jl
Jordi Manyer, Jai Tushar, Santiago Badia
Hybrid finite element methods such as hybridizable discontinuous Galerkin, hybrid high-order and weak Galerkin have emerged as powerful techniques for solving partial differential…
Geometric Multigrid solvers for Hybrid High-Order methods on polytopal meshes
Santiago Badia, Jordi Manyer
We propose the first optimal geometric multigrid solver for hybrid high-order discretizations that can handle arbitrary polytopal agglomeration hierarchies in both two and three di…
Energy minimisation using overlapping tensor-product free-knot B-splines
Alexandre Magueresse, Santiago Badia
Accurately solving PDEs with localised features requires refined meshes that adapt to the solution. Traditional numerical methods, such as finite elements, are linear in nature and…
A convergence framework for energy minimisation of linear self-adjoint elliptic PDEs in nonlinear approximation spaces
Alexandre Magueresse, Santiago Badia
Recent years have seen the emergence of nonlinear methods for solving partial differential equations (PDEs), such as physics-informed neural networks (PINNs). While these approache…