Related papers: Stabilization techniques for immersogeometric anal…
We study a fictitious domain approach with Lagrange multipliers to discretize Stokes equations on a mesh that does not fit the boundaries. A mixed finite element method is used for fluid flow. Several stabilization terms are added to…
In this thesis we develop a stabilised finite element method for solving the equations of poroelasticity to enable solving complex models of biological tissues such as the human lungs. For the proposed numerical scheme, we use the lowest…
We develop a general framework for construction and analysis of discrete extension operators with application to unfitted finite element approximation of partial differential equations. In unfitted methods so called cut elements intersected…
In this work, we propose a novel formulation for the solution of partial differential equations using finite element methods on unfitted meshes. The proposed formulation relies on the discrete extension operator proposed in the aggregated…
The Reynolds equation, combined with the Elrod algorithm for including the effect of cavitation, resembles a nonlinear convection-diffusion-reaction (CDR) equation. Its solution by finite elements is prone to oscillations in…
The paper introduces an adaptive version of the stabilized Trace Finite Element Method (TraceFEM) designed to solve low-regularity elliptic problems on level-set surfaces using a shape-regular bulk mesh in the embedding space. Two…
Laminated glass units exhibit complex response as a result of different mechanical behavior and properties of glass and polymer foil. We aim to develop a finite element model for elastic laminated glass plates based on the refined plate…
Explicit expressions, for efficient application in engineering practice, are derived for generalized displacements and stresses in simply supported multi-layered wide plates and beams subjected to steady-state thermal and mechanical…
This work provides an efficient virtual element scheme for the modeling of nonlinear elastodynamics undergoing large deformations. The virtual element method (VEM) has been applied to various engineering problems such as elasto-plasticity,…
Shells are ubiquitous thin structures that can undergo large nonlinear elastic deformations while exhibiting combined modes of bending and stretching, and have profound modern applications. In this paper, we have proposed a new Isogeometric…
In many applications, the governing PDE to be solved numerically contains a stiff component. When this component is linear, an implicit time stepping method that is unencumbered by stability restrictions is often preferred. On the other…
The Landau collision integral is often considered the gold standard in the context of kinetic plasma simulation due to its conservative properties, despite challenges involved in its discretization. The primary challenge when implementing…
We propose an adaptive polygonal finite element formulation for collapse plastic analysis of solids. The article contributes into four crucial points: 1) Wachspress shape functions at vertex and bubble nodes handled at a primal-mesh level;…
We consider a finite element method with symmetric stabilisation for the discretisation of the transient convection--diffusion equation. For the time-discretisation we consider either the second order backwards differentiation formula or…
We propose a mathematical model that combines elastic, viscous and porous effects with growth or shrinkage due to microstructural changes. This phenomenon is important in tissue or tumor growth, as well as in dermal contraction. Although…
Stiffness degradation and progressive failure of composite laminates are complex processes involving evolution and multi-mode interactions among fiber fractures, intra-ply matrix cracks and inter-ply delaminations. This paper presents a…
This is a study of certain finite element methods designed for convection-dominated, time-dependent partial differential equations. Specifically, we analyze high order space-time tensor product finite element discretizations, used in a…
In this paper, we study a numerical method for the solution of partial differential equations on evolving surfaces. The numerical method is built on the stabilized trace finite element method (TraceFEM) for the spatial discretization and…
We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions and intersections within the material, a geometry of…
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…