English
Related papers

Related papers: A multiscale method for heterogeneous bulk-surface…

200 papers

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…

Numerical Analysis · Mathematics 2025-08-12 Brittany A. Erickson

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…

Computational Engineering, Finance, and Science · Computer Science 2024-05-24 Pere A. Martorell , Santiago Badia

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…

Numerical Analysis · Mathematics 2023-10-16 Martin Averseng , Xavier Claeys , Ralf Hiptmair

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…

Numerical Analysis · Mathematics 2023-02-14 Markus Bause , Mathias Anselmann , Uwe Köcher , Florin A. Radu

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,…

Dynamical Systems · Mathematics 2019-11-18 Chen Chen , A. J. Roberts , J. E. Bunder

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…

Numerical Analysis · Mathematics 2015-08-11 Donald L. Brown , Maria Vasilyeva

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…

Numerical Analysis · Mathematics 2014-02-03 Rui M. P. Almeida , José C. M. Duque , Jorge Ferreira , Rui J. Robalo

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…

Analysis of PDEs · Mathematics 2016-11-08 Charles M. Elliott , Thomas Ranner , Chandrasekhar Venkataraman

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…

Numerical Analysis · Mathematics 2014-03-27 Erik Burman , Peter Hansbo , Mats G. Larson , Sara Zahedi

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…

Numerical Analysis · Mathematics 2021-12-28 Zhihao Ge , Wenlong He

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…

Numerical Analysis · Mathematics 2024-04-22 Thomas Führer , Diego Paredes

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…

Numerical Analysis · Mathematics 2026-01-12 Alessandro Contri , André Massing , Padmini Rangamani

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…

Numerical Analysis · Mathematics 2015-08-03 Mukesh Kumar , S. Chandra Sekhara Rao

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.

Numerical Analysis · Mathematics 2021-11-01 Susanne C. Brenner , José C. Garay , Li-yeng Sung

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…

Computational Physics · Physics 2021-08-26 Nathan G. March , Elliot J. Carr , Ian W. Turner

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…

Fluid Dynamics · Physics 2023-03-22 Pei Zhang , Ling Qiu , S. A. Galindo-Torres , Yilin Chen , A. Scheuermann , Ling Li

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…

Numerical Analysis · Mathematics 2024-12-17 Aaron Pim , Tristan Pryer , Alex Trenam

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…

Numerical Analysis · Mathematics 2012-09-03 Karin Saavedra , Olivier Allix , Pierre Gosselet

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…

Numerical Analysis · Mathematics 2021-11-17 Gustav Ludvigsson , Kyle R. Steffen , Simon Sticko , Siyang Wang , Qing Xia , Yekaterina Epshteyn , Gunilla Kreiss