Related papers: Polyhedral Discretizations for Elliptic PDEs
We propose two new strategies based on Machine Learning techniques to handle polyhedral grid refinement, to be possibly employed within an adaptive framework. The first one employs the k-means clustering algorithm to partition the points of…
We present a new discretization method for homogeneous convection-diffusion-reaction boundary value problems in 3D that is a non-standard finite element method with PDE-harmonic shape functions on polyhedral elements. The element stiffness…
This work explores the potential of spatial model checking of polyhedral models on a number of selected examples. In computer graphics polyhedral models can be found in the form of triangular surface meshes of tetrahedral volume meshes…
The virtual element method (VEM) allows discretization of the problem domain with polygons in 2D. The polygons can have an arbitrary number of sides and can be concave or convex. These features, among others, are attractive for meshing…
Smoothed particle hydrodynamics (SPH) has been extensively used to model high and low Reynolds number flows, free surface flows and collapse of dams, study pore-scale flow and dispersion, elasticity, and thermal problems. In different…
In this study, we propose a virtual element scheme to solve the Darcy problem in three physical dimensions. The main novelty, here proposed, is that curved elements are naturally handled without any degradation of the solution accuracy. In…
We numerically validate the Virtual Element Method of order k for general second order elliptic problems with variable coefficients in three dimensions. Moreover, we investigate numerically also the Serendipity version of the VEM (in three…
We prove that for compactly perturbed elliptic problems, where the corresponding bilinear form satisfies a Garding inequality, adaptive mesh-refinement is capable of overcoming the preasymptotic behavior and eventually leads to convergence…
The biharmonic equation with Dirichlet and Neumann boundary conditions discretized using the mixed finite element method and piecewise linear (with the possible exception of boundary triangles) finite elements on triangular elements has…
In this work we propose a new, arbitrary order space-time finite element discretisation for Hamiltonian PDEs in multisymplectic formulation. We show that the new method which is obtained by using both continuous and discontinuous…
Diffeomorphic matching (only one of several names for this technique) is a technique for non-rigid registration of curves and surfaces in which the curve or surface is embedded in the flow of a time-series of vector fields. One seeks the…
Flow in fractured porous media represents a challenge for discretization methods due to the disparate scales and complex geometry. Herein we propose a new discretization, based on the mixed finite element method and mortar methods. Our…
The present work develops hybrid multigrid methods for high-order discontinuous Galerkin discretizations of elliptic problems. Fast matrix-free operator evaluation on tensor product elements is used to devise a computationally efficient PDE…
We present a new framework for expressing finite element methods on multiple intersecting meshes: multimesh finite element methods. The framework enables the use of separate meshes to discretize parts of a computational domain that are…
Adaptive mesh refinement techniques are nowadays an established and powerful tool for the numerical discretization of PDE's. In recent years, wavelet bases have been proposed as an alternative to these techniques. The main motivation for…
This document contains working annotations on the Virtual Element Method (VEM) for the approximate solution of diffusion problems with variable coefficients. To read this document you are assumed to have familiarity with concepts from the…
A discretisation scheme that preserves topological features of a physical problem is extended so that differential geometric structures can be approximated in a consistent way thus giving access to the study of physical systems which are…
We give an abstract formulation of the formal theory partial differential equations (PDEs) in synthetic differential geometry, one that would seamlessly generalize the traditional theory to a range of enhanced contexts, such as…
The finite element method can be viewed as a machine that automates the discretization of differential equations, taking as input a variational problem, a finite element and a mesh, and producing as output a system of discrete equations.…
A new parametric surface representation is proposed that interpolates the vertices of a given closed mesh of arbitrary topology. Smoothly connecting quadrilateral patches are created by blending local, multi-sided quadratic interpolants. In…