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A fully discrete finite element method, based on a new weak formulation and a new time-stepping scheme, is proposed for the surface diffusion flow of closed curves in the two-dimensional plane. It is proved that the proposed method can…
We present a novel hyperviscosity formulation for stabilizing RBF-FD discretizations of the advection-diffusion equation. The amount of hyperviscosity is determined quasi-analytically for commonly-used explicit, implicit, and…
In this paper, we investigate the combination of a linear continuous interior penalty type and a non-linear artificial diffusion stabilisation applied to the transport problem, based on continuous Galerkin finite elements in space. This…
Since the 1960's the finite element method emerged as a powerful tool for the numerical simulation of countless physical phenomena or processes in applied sciences. One of the reasons for this undeniable success is the great versatility of…
This article is the first part of a two-fold study, the objective of which is the theoretical analysis and numerical investigation of new approximate corrector problems in the context of stochastic homogenization. We present here three new…
We consider an elliptic partial differential equation in non-divergence form with a random diffusion matrix and random forcing term. To address this, we propose a mixed-type continuous finite element discretization in the physical domain,…
The localized artificial diffusivity (LAD) method is widely regarded as the preferred multi-material regularization scheme for the compact finite difference method, because it is conservative, easy to implement, and generally robust for a…
We propose a change of variable approach and discontinuity capturing methods to ensure physical constraints for advection-reaction equations discretized by the finite element method. This change of variable confines the concentration below…
In this thesis, we investigate a novel local projection based stabilized conforming virtual element method for the generalized Oseen problem using equal-order element pairs on general polygonal meshes. To ensure the stability, particularly…
A fractional diffusion equation with advection term is rigorously derived from a kinetic transport model with a linear turning operator, featuring a fat-tailed equilibrium distribution and a small directional bias due to a given vector…
In this work we propose a nonlinear stabilization technique for convection-diffusion-reaction and pure transport problems discretized with space-time isogeometric analysis. The stabilization is based on a graph-theoretic artificial…
In this paper, we study the diffusion approximation for singularly perturbed stochastic reaction-diffusion equation with a fast oscillating term. The asymptotic limit for the original system is obtained, where an extra Gaussian term…
This paper is concerned with numerical solution of transport problems in heterogeneous porous media. A semi-discrete continuous-in-time formulation of the linear advection-diffusion equation is obtained by using a mixed hybrid finite…
In this paper, a modification of the conventional approximations to the quasi-maximum likelihood method is introduced for the parameter estimation of diffusion processes from discrete observations. This is based on a convergent…
This paper presents an initial exploration of stress-assisted diffusion problems in three dimensions within the framework of the virtual element method (VEM). Hilbert spaces enriched with parameter-weighted norms, the extended…
In this paper we consider a model singularly perturbed convection diffusion problem which is solved by a streamline diffusion finite element method (SDFEM) on a Shishkin rectangular mesh. To put insight into the influences of stabilization…
We present a finite element discretisation to model the interaction between a poroelastic structure and an elastic medium. The consolidation problem considers fully coupled deformations across an interface, ensuring continuity of…
In this paper, the pressure correctionfinite element method is proposed for the 2D/3D time-dependent thermomicropolarfluid equations. Thefirst-order and second-order backward difference formulas (BDF) are adopted to approximate the time…
We develop a stabilized cut finite element method for the convection problem on a surface based on continuous piecewise linear approximation and gradient jump stabilization terms. The discrete piecewise linear surface cuts through a…
Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…