Related papers: An isogeometric finite element formulation for pha…
Numerical simulations of brittle fracture using phase-field approaches often employ a discrete approximation framework that applies the same order of interpolation for the displacement and phase-field variables. Most common is to use linear…
The motivation of this work is to produce an integrated formulation for material response due to detonation wave loading. Here, we focus on elastoplastic structural response. In particular, we are interested to capture miscible and…
Consider a model of particles (nucleons) which has a two-body interaction which leads to bound composites with saturation properties. These properties are : all composites have the same density and the ground state energies of composites…
We propose a new numerical method to solve the Cahn-Hilliard equation coupled with non-linear wetting boundary conditions. We show that the method is mass-conservative and that the discrete solution satisfies a discrete energy law similar…
We consider within a finite element approach the usage of different adaptively refined meshes for different variables in systems of nonlinear, time-depended PDEs. To resolve different solution behaviours of these variables, the meshes can…
Chaotic free surface flows are challenging problems to simulate numerically, mainly due to the significant changes in geometry and frequent topological changes. Methods that track the evolution of the fluid in a Lagrangian formulation are a…
In this paper we devise and analyze a mixed finite element method for a modified Cahn-Hilliard equation coupled with a non-steady Darcy-Stokes flow that models phase separation and coupled fluid flow in immiscible binary fluids and diblock…
In fractured natural formations, the equations governing fluid flow and geomechanics are strongly coupled. Hydrodynamical properties depend on the mechanical configuration, and they are therefore difficult to accurately resolve using…
Finite element simulations have been used to solve various partial differential equations (PDEs) that model physical, chemical, and biological phenomena. The resulting discretized solutions to PDEs often do not satisfy requisite physical…
This paper is concerned with finite element approximations of $W^{2,p}$ strong solutions of second-order linear elliptic partial differential equations (PDEs) in non-divergence form with continuous coefficients. A nonstandard (primal)…
Problems of interest in hydrogeology and hydrocarbon resources involve complex heterogeneous geological formations. Such domains are most accurately represented in reservoir simulations by unstructured computational grids. Finite element…
We consider numerical simulation of the isotropic elastic wave equations arising from seismic applications with non-trivial land topography. The more flexible finite element method is applied to the shallow region of the simulation domain…
We present an approach to robustly track the geometry of an object that deforms over time from a set of input point clouds captured from a single viewpoint. The deformations we consider are caused by applying forces to known locations on…
The analysis of electromagnetic scattering has long been performed on a discrete representation of the geometry. This representation is typically continuous but {\em not} differentiable. The need to define physical quantities on this…
We present a hybrid mimetic finite-difference and virtual element formulation for coupled single-phase poromechanics on unstructured meshes. The key advantage of the scheme is that it is convergent on complex meshes containing highly…
We propose and analyze volume-preserving parametric finite element methods for surface diffusion, conserved mean curvature flow and an intermediate evolution law in an axisymmetric setting. The weak formulations are presented in terms of…
We present a new fixed mesh algorithm for solving a class of interface inverse problems for the typical elliptic interface problems. These interface inverse problems are formulated as shape optimization prob- lems whose objective…
This work presents a rigorous prediction of the effective equations governing the paramagnetic-ferromagnetic phase transition in a perforated three-dimensional body. Assuming a periodic distribution of perforations, we investigate the…
We study the coupled surface and grain boundary motion in a bicrystal in the context of the "quarter loop" geometry. Two types of physics motions are involved in this model: motion by mean curvature and motion by surface diffusion. The goal…
In this paper, we develop a multiphysics finite element method for solving the quasi-static thermo-poroelasticity model with nonlinear permeability. The model involves multiple physical processes such as deformation, pressure, diffusion and…