Related papers: Isoparametric Virtual Element Methods
This paper presents an iterative method suitable for inverting semilinear problems which are important kernels in many numerical applications. The primary idea is to employ a parametrization that is able to reduce semilinear problems into…
This paper analyzes two eXtended finite element methods (XFEMs) for linear quadratic optimal control problems governed by Poisson equation in non-convex domains. We follow the variational discretization concept to discretize the continuous…
We consider adaptive finite element methods for second-order elliptic PDEs, where the arising discrete systems are not solved exactly. For contractive iterative solvers, we formulate an adaptive algorithm which monitors and steers the…
We extend the basic idea of Serendipity Virtual Elements from the previous case (by the same authors) of nodal ($H^1$-conforming) elements, to a more general framework. Then we apply the general strategy to the case of $H(div)$ and…
We construct a nonconforming virtual element method (ncVEM) based on approximation spaces that are enriched with special singular functions. This enriched ncVEM is tailored for the approximation of solutions to elliptic problems, which have…
Meshing complex engineering domains is a challenging task. Arbitrary polyhedral meshes can provide the much needed flexibility in automated discretization of such domains. The geometric property of the polyhedral meshes such as the…
In this work, we discuss and compare three methods for the numerical approximation of constant- and variable-coefficient diffusion equations in both single and composite domains with possible discontinuity in the solution/flux at…
We present a space-time virtual element method for the discretization of the heat equation, which is defined on general prismatic meshes and variable degrees of accuracy. Strategies to handle efficiently the space-time mesh structure are…
In this work, we investigate the numerical approximation of the second order non-autonomous semilnear parabolic partial differential equation (PDE) using the finite element method. To the best of our knowledge, only the linear case is…
We describe a variational approximation method for efficient inference in large-scale probabilistic models. Variational methods are deterministic procedures that provide approximations to marginal and conditional probabilities of interest.…
We introduce and analyze a virtual element method (VEM) for the Helmholtz problem with approximating spaces made of products of low order VEM functions and plane waves. We restrict ourselves to the 2D Helmholtz equation with impedance…
The goal of this paper is to develop a numerical algorithm that solves a two-dimensional elliptic partial differential equation in a polygonal domain using tensor methods and ideas from isogeometric analysis. The proposed algorithm is based…
Coefficient inverse problems related to identifying the right-hand side of an equation with use of additional information is of interest among inverse problems for partial differential equations. When considering non-stationary problems,…
A finite element methodology for large classes of variational boundary value problems is defined which involves discretizing two linear operators: (1) the differential operator defining the spatial boundary value problem; and (2) a Riesz…
We study the use of Temporal-Difference learning for estimating the structural parameters in dynamic discrete choice models. Our algorithms are based on the conditional choice probability approach but use functional approximations to…
This paper presents a novel multi-scale method for elliptic partial differential equations with arbitrarily rough coefficients. In the spirit of numerical homogenization, the method constructs problem-adapted ansatz spaces with uniform…
The mesh flexibility offered by the virtual element method through the permission of arbitrary element geometries, and the seamless incorporation of `hanging' nodes, has made the method increasingly attractive in the context of adaptive…
The finite element method(FEM) is applied to bound leading eigenvalues of Laplace operator over polygonal domain. Compared with classical numerical methods, most of which can only give concrete eigenvalue bounds over special domain of…
In this paper we present an algebraic dimension-oblivious two-level domain decomposition solver for discretizations of elliptic partial differential equations. The proposed parallel solver is based on a space-filling curve partitioning…
This paper analyses the nonconforming Morley type virtual element method to approximate a regular solution to the von K\'{a}rm\'{a}n equations that describes bending of very thin elastic plates. Local existence and uniqueness of a discrete…