Related papers: Patch bubbles for advection-dominated steady and u…
An adapted bubble approach which is a modifiation of the residual-free bubbles (RFB) method, is proposed for the Helmhotz problem in 2D. A new two-level finite element method is introduced for the approximations of the bubble functions.…
We present an investigation of the Residual Free Bubble finite element method for a class of multiscale nonlinear elliptic partial differential equations. After proposing a nonlinear version for the method, we address fundamental questions…
We present error estimates for the BMZ (Bubble Mesh Zoom) residual-free bubble method applied to a convection-diffusion equation in the convection-dominated regime. The method incorporates both element bubbles and residual-free bubbles…
An improved numerical scheme is proposed for advection-dominated advection-diffusion problem. The scheme is based on Galerkin finite element method (FEM) with basis enriched with approximations to residual-free bubbles. The stabilisation…
In this work, we investigate (energy) stability of global radial basis function (RBF) methods for linear advection problems. Classically, boundary conditions (BC) are enforced strongly in RBF methods. By now it is well-known that this can…
Optimally convergent (with respect to the regularity) quadratic finite element method for two dimensional obstacle problem on simplicial meshes is studied in (Brezzi, Hager, Raviart, Numer. Math, 28:431--443, 1977). There was no analogue of…
The paper develops a hybrid method for solving a system of advection--diffusion equations in a bulk domain coupled to advection--diffusion equations on an embedded surface. A monotone nonlinear finite volume method for equations posed in…
Liquid simulations for computer animation often avoid simulating the air phase to reduce computational costs and ensure good conditioning of the linear systems required to enforce incompressibility. However, this free surface assumption…
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…
This work proposes a novel shape optimization framework for geometric inverse problems governed by the advection--diffusion equation, based on the coupled complex boundary method (CCBM). Building on recent developments [Afr22, Rab23, Rab25,…
This paper presents an enhancement to the free surface lattice Boltzmann method (FSLBM) for the simulation of bubbly flows including rupture and breakup of bubbles. The FSLBM uses a volume of fluid approach to reduce the problem of a…
We propose enforcing constraints on Model-Based Diffusion by introducing emerging barrier functions inspired by interior point methods. We demonstrate that the standard Model-Based Diffusion algorithm can lead to catastrophic performance…
We present a novel artificial diffusion method to circumvent the instabilities associated with the standard finite element approximation of convection-diffusion equations. Motivated by the micromorphic approach, we introduce an auxiliary…
In order to model the Fermi bubbles we apply the theory of the superbubble (SB). A thermal model and a self-gravitating model are reviewed. We introduce a third model based on the momentum conservation of a thin layer which propagates in a…
We consider mixing problems in the form of transient convection--diffusion equations with a velocity vector field with multiscale character and rough data. We assume that the velocity field has two scales, a coarse scale with slow spatial…
We present a high-order radial basis function finite difference (RBF-FD) framework for the solution of advection-diffusion equations on time-varying domains. Our framework is based on a generalization of the recently developed Overlapped…
Meshless solution to differential equations using radial basis functions (RBF) is an alternative to grid based methods commonly used. Since the meshless method does not need an underlying connectivity in the form of control volumes or…
PDE-constrained optimization problems have been barely solved by radial basis functions (RBFs) methods [Pearson, 2013]. It is well known that RBF methods can attain an exponential rate of convergence when $C^{\infty}$ kernels are used,…
In this paper, we present a meshless hybrid method combining the Generalized Finite Difference (GFD) and Finite Difference based Radial Basis Function (RBF-FD) approaches to solve non-homogeneous partial differential equations (PDEs)…
There is a wide range of stabilized finite element methods for stationary and non-stationary convection-diffusion equations such as streamline diffusion methods, local projection schemes, subgrid-scale techniques, and continuous interior…