Related papers: Mesh Quality Metrics for Isogeometric Bernstein-B\…
We introduce an integrated meshing and finite element method pipeline enabling black-box solution of partial differential equations in the volume enclosed by a boundary representation. We construct a hybrid hexahedral-dominant mesh, which…
In recent papers the author introduced a simple alternative to isoparametric finite elements of the n-simplex type, to enhance the accuracy of approximations of second-order boundary value problems with Dirichlet conditions, posed in smooth…
We introduce the isogeometric shape optimisation of thin shell structures using subdivision surfaces. Both triangular Loop and quadrilateral Catmull-Clark subdivision schemes are considered for geometry modelling and finite element…
A Petrov-Galerkin finite element method is constructed for a singularly perturbed elliptic problem in two space dimensions. The solution contains a regular boundary layer and two characteristic boundary layers. Exponential splines are used…
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…
The Poisson-Boltzmann equation is a widely used model to study the electrostatics in molecular solvation. Its numerical solution using a boundary integral formulation requires a mesh on the molecular surface only, yielding accurate…
Mesh adaptivity is a technique to provide detail in numerical solutions without the need to refine the mesh over the whole domain. Mesh adaptivity in isogeometric analysis can be driven by Truncated Hierarchical B-splines (THB-splines)…
In this paper, gradient-based optimization methods are combined with finite-element modeling for improving electric devices. Geometric design parameters are considered by affine decomposition of the geometry or by the design element…
This work introduces a novel discontinuity-tracking framework for resolving discontinuous solutions of conservation laws with high-order numerical discretizations that support inter-element solution discontinuities, such as discontinuous…
We present a new approach to discretizing shape optimization problems that generalizes standard moving mesh methods to higher-order mesh deformations and that is naturally compatible with higher-order finite element discretizations of…
Mesh optimization procedures are generally a combination of node smoothing and discrete operations which affect a small number of elements to improve the quality of the overall mesh. These procedures are useful as a post-processing step in…
We present an optimization procedure for generic polygonal or polyhedral meshes, tailored for the Virtual Element Method (VEM). Once the local quality of the mesh elements is analyzed through a quality indicator specific to the VEM, groups…
In this paper we consider finite element approaches to computing the mean curvature vector and normal at the vertices of piecewise linear triangulated surfaces. In particular, we adopt a stabilization technique which allows for first order…
A higher-order accurate finite element method is proposed which uses automatically generated meshes based on implicit level-set data for the description of boundaries and interfaces in two and three dimensions. The method is an alternative…
Fitted finite element methods are constructed for a singularly perturbed convection-diffusion problem in two space dimensions. Exponential splines as basis functions are combined with Shishkin meshes to obtain a stable parameter-uniform…
As an important metric for mesh quality evaluation, the isotropy property holds significant value for applications such as texture UV-mapping, physical simulation, and discrete geometric analysis. Classical isotropy remeshing methods adjust…
Obtaining high-precision guaranteed lower eigenvalue bounds remains difficult, even though the standard high-order conforming finite element (FEM) easily yields extremely sharp upper bounds. Recently developed rigorous approaches using such…
Computational meshes arising from shape optimization routines commonly suffer from decrease of mesh quality or even destruction of the mesh. In this work, we provide an approach to regularize general shape optimization problems to increase…
In this contribution we develop a cut finite element method with boundary value correction of the type originally proposed by Bramble, Dupont, and Thomee. The cut finite element method is a fictitious domain method with Nitsche type…
A new concept for the higher-order accurate approximation of partial differential equations on manifolds is proposed where a surface mesh composed by higher-order elements is automatically generated based on level-set data. Thereby, it…