Related papers: On surface meshes induced by level set functions
We propose a method that morphs high-orger meshes such that their boundaries and interfaces coincide/align with implicitly defined geometries. Our focus is particularly on the case when the target surface is prescribed as the zero…
In the framework of displacement-based equivalent single layer (ESL) plate theories for laminates, this paper presents a generic and automatic method to extend a basis higher-order shear deformation theory (polynomial, trigonometric,…
We prove a stochastic homogenization result for integral functionals defined on finite partitions assuming the surface tension to be stationary and possibly ergodic. We also consider the convergence of boundary value problems when we impose…
Finite element approximations of minimal surface are not always precise. They can even sometimes completely collapse. In this paper, we provide a simple and inexpensive method, in terms of computational cost, to improve finite element…
We develop a Nitsche-based formulation for a general class of stabilized finite element methods for the Stokes problem posed on a pair of overlapping, non-matching meshes. By ex- tending the least-squares stabilization to the overlap…
We study harmonic surfaces in $\mathbb{R}^3$ through the framework of harmonic Enneper immersions and prove a superposition principle for such surfaces. We prove that minimal and maximal surfaces admit a decomposition into harmonic…
In this paper we consider a coupled bulk-surface PDE in two space dimensions. The model consists of a PDE in the bulk that is coupled to another PDE on the surface through general nonlinear boundary conditions. For such a system we propose…
The paper introduces a finite element method for the incompressible Navier--Stokes equations posed on a closed surface $\Gamma\subset\R^3$. The method needs a shape regular tetrahedra mesh in $\mathbb{R}^3$ to discretize equations on the…
Consider the Poisson equation with the Dirichlet boundary condition on a three-dimensional polyhedral domain. For singular solutions from the non-smoothness of the domain boundary, we propose new anisotropic tetrahedral mesh refinement…
The formulation of a new prism finite element is presented for the nonlinear analysis of solid shells subject to large strains and large displacements. The element is based on hierarchical, heterogeneous, and anisotropic shape functions. As…
This paper introduces discrete differential form spaces over two-dimensional manifold meshes that feature enhanced subdivision-induced inter-element regularity compared to conventional finite element (FE) spaces. This increase in smoothness…
The thin plate spline, as introduced by Duchon, interpolates a smooth surface through scattered data. It is computationally expensive when there are many data points. The finite element thin plate spline (TPSFEM) possesses similar smoothing…
For most finite element simulations, boundary-conforming meshes have significant advantages in terms of accuracy or efficiency. This is particularly true for complex domains. However, with increased complexity of the domain, generating a…
In this work, we investigate the performance CutFEM as a high fidelity solver as well as we construct a competent and economical reduced order solver for PDE-constrained optimization problems in parametrized domains that live in a fixed…
It is natural to expect the following loosely stated approximation principle to hold: a numerical approximation solution should be in some sense as smooth as its target exact solution in order to have optimal convergence. For piecewise…
In this paper we establish a gap phenomenon for immersed surfaces with arbitrary codimension, topology and boundaries that satisfy one of a family of systems of fourth-order anisotropic geometric partial differential equations. Examples…
Convex optimization problems arising in applications often have favorable objective functions and complicated constraints, thereby precluding first-order methods from being immediately applicable. We describe an approach that exchanges the…
Given a noncompact disconnected complete periodic curve $\Gamma$ with no self intersection in $\mathbb R^3$, it is proved that there exists a noncompact simply connected periodic minimal surface spanning $\Gamma$. As an application it is…
In this article we consider a priori error and pointwise estimates for finite element approximations of solutions to semilinear elliptic boundary value problems in d>=2 space dimensions, with nonlinearities satisfying critical growth…
A set of locally finite perimeter $E \subset \mathbb{R}^{n}$ is called an anisotropic minimal surface in an open set $A$ if $\Phi(E;A) \le \Phi(F;A)$ for some surface energy $\Phi(E;A) = \int_{\partial^{*}E \cap A} \| \nu_{E}\| d…