اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدThe nonconforming Trefftz virtual element method: general setting, applications, and dispersion analysis for the Helmholtz equation
92
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We present a survey of the nonconforming Trefftz virtual element method for the Laplace and Helmholtz equations. For the latter, we present a new abstract analysis, based on weaker assumptions on the stabilization, and numerical results on the dispersion analysis, including comparison with the plane wave discontinuous Galerkin method.
قيم البحث
اقرأ أيضاً
We address the issue of designing robust stabilization terms for the nonconforming virtual element method. To this end, we transfer the problem of defining the stabilizing bilinear form from the elemental nonconforming virtual element space, whose fu
nctions are not known in closed form, to the dual space spanned by the known functionals providing the degrees of freedom. By this approach, we manage to construct different bilinear forms yielding optimal or quasi-optimal stability bounds and error estimates, under weaker assumptions on the tessellation than the ones usually considered in this framework. In particular, we prove optimality under geometrical assumptions allowing a mesh to have a very large number of arbitrarily small edges per element. Finally, we numerically assess the performance of the VEM for several different stabilizations fitting with our new framework on a set of representative test cases.
We introduce the nonconforming Virtual Element Method (VEM) for the approximation of second order elliptic problems. We present the construction of the new element in two and three dimensions, highlighting the main differences with the conforming V
EM and the classical nonconforming finite element methods. We provide the error analysis and establish the equivalence with a family of mimetic finite difference methods.
We deal with the Finite Element Tearing and Interconnecting Dual Primal (FETI-DP) preconditioner for elliptic problems discretized by the virtual element method (VEM). We extend the result of [22] to the three dimensional case. We prove polylogarithm
ic condition number bounds, independent of the number of subdomains, the mesh size, and jumps in the diffusion coefficients. Numerical experiments validate the theory
In this paper we consider the Virtual Element discretization of a minimal surface problem, a quasi-linear elliptic partial differential equation modeling the problem of minimizing the area of a surface subject to a prescribed boundary condition. We d
erive optimal error estimate and present several numerical tests assessing the validity of the theoretical results.
We design and analyze a coupling of a discontinuous Galerkin finite element method with a boundary element method to solve the Helmholtz equation with variable coefficients in three dimensions. The coupling is realized with a mortar variable that is
related to an impedance trace on a smooth interface. The method obtained has a block structure with nonsingular subblocks. We prove quasi-optimality of the $h$- and $
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
