5 papers
Parameter-robust well-posedness and discretisation for coupled Darcy--Forchheimer and advection-diffusion-reaction equations
Rishi Das, Harsha Hutridurga, Amiya K. Pani +1
We adapt the recent theory for unique solvability of perturbed saddle-point problems in Banach spaces to the case of parameter-independent stability bounds. This also constitutes a…
Divergence-free unfitted finite element discretisations for the Darcy problem
Santiago Badia, Anne Boschman, Alberto F. MartÃn +3
We develop an unfitted compatible finite element discretisation for the Darcy problem based on -conforming flux spaces and discontinuous pressure spaces. The metho…
A Residual Minimization approach for Nonlinear Partial Differential Equations set in Banach spaces
Ignacio Muga, Jorge Perera, Sergio Rojas +1
In this work, we propose and analyze a residual-minimization strategy for the numerical solution of nonlinear PDEs posed in Banach spaces. Given a finite-dimensional trial space an…
Perturbed saddle-point problems in with non-regular loads
Abeer F. Alsohaim, Tomas Führer, Ricardo Ruiz-Baier +1
In this work, we develop the discrete solvability analysis for perturbed saddle-point problems in Banach spaces with forcing terms regularised by means of a projector constructed u…
An ultra-weak three-field finite element formulation for the biharmonic and extended Fisher--Kolmogorov equations
Rekha Khot, Bishnu P. Lamichhane, Ricardo Ruiz-Baier
This paper discusses a so-called ultra-weak three-field formulation of the biharmonic problem where the solution, its gradient, and an additional Lagrange multiplier are the three…