Related papers: A multiscale method for heterogeneous bulk-surface…
In this work we explore the fidelity of numerical approximations to the analytic spectra of hyperbolic partial differential equation systems with variable coefficients. We are particularly interested in the ability of discrete methods to…
We show that in the variational multiscale framework, the weak enforcement of essential boundary conditions via Nitsche's method corresponds directly to a particular choice of projection operator. The consistency, symmetry and penalty terms…
When modeling scientific and industrial problems, geometries are typically modeled by explicit boundary representations obtained from computer-aided design software. Unfitted (also known as embedded or immersed) finite element methods offer…
We present a preconditioning method for the linear systems arising from the boundary element discretization of the Laplace hypersingular equation on a $2$-dimensional triangulated surface $\Gamma$ in $\mathbb{R}^3$. We allow $\Gamma$ to…
We study the numerical approximation by space-time finite element methods of a multi-physics system coupling hyperbolic elastodynamics with parabolic transport and modeling poro- and thermoelasticity. The equations are rewritten as a…
Multiscale modelling aims to systematically construct macroscale models of materials with fine microscale structure. However, macroscale boundary conditions are typically not systematically derived, but rely on heuristic arguments,…
In this paper, we consider the numerical solution of some nonlinear poroelasticity problems that are of Biot type and develop a general algorithm for solving nonlinear coupled systems. We discuss the difficulties associated with flow and…
The aim of this paper is to establish the convergence and error bounds to the fully discrete solution for a class of nonlinear systems of reaction-diffusion nonlocal type with moving boundaries, using a linearized Crank-Nicolson-Galerkin…
We consider a coupled bulk-surface system of partial differential equations with nonlinear coupling modelling receptor-ligand dynamics. The model arises as a simplification of a mathematical model for the reaction between cell surface…
We develop a cut finite element method for a second order elliptic coupled bulk-surface model problem. We prove a priori estimates for the energy and $L^2$ norms of the error. Using stabilization terms we show that the resulting algebraic…
In this paper, we propose a multiphysics finite element method for a nonlinear poroelasticity model. To better describe the processes of deformation and diffusion, we firstly reformulate the nonlinear fluid-solid coupling problem into a…
For a reaction-dominated diffusion problem we study a primal and a dual hybrid finite element method where weak continuity conditions are enforced by Lagrange multipliers. Uniform robustness of the discrete methods is achieved by enriching…
Cellular morphodynamics requires solving systems of coupled partial differential equations on moving bulk and surface domains, where advection-dominant transport, structure preservation, and severe mesh distortions make robust simulation…
We present a high order parameter-robust numerical method for a system of (M>=2) coupled singularly perturbed parabolic reaction-diffusion problems. A small perturbation parameter {\epsilon} is multiplied with the second order spatial…
We investigate multiscale finite element methods for an elliptic distributed optimal control problem with rough coefficients. They are based on the (local) orthogonal decomposition methodology of M\aa lqvist and Peterseim.
Computational modelling of diffusion in heterogeneous media is prohibitively expensive for problems with fine-scale heterogeneities. A common strategy for resolving this issue is to decompose the domain into a number of non-overlapping…
Fluid-particle systems are very common in many natural processes and engineering applications. However, accurately and efficiently modelling fluid-particle systems with complex particle shapes is still a challenging task. Here, we present a…
This work addresses an optimal control problem constrained by a degenerate kinetic equation of parabolic-hyperbolic type. Using a hypocoercivity framework we establish the well-posedness of the problem and demonstrate that the optimal…
This paper investigates a computational strategy for studying the interactions between multiple through-the-width delaminations and global or local buckling in composite laminates taking into account possible contact between the delaminated…
In this work, we discuss and compare three methods for the numerical approximation of constant- and variable-coefficient diffusion equations in both single and composite domains with possible discontinuity in the solution/flux at…