14 research outputs found
A Two-Level Method for Mimetic Finite Difference Discretizations of Elliptic Problems
We propose and analyze a two-level method for mimetic finite difference
approximations of second order elliptic boundary value problems. We prove that
the two-level algorithm is uniformly convergent, i.e., the number of iterations
needed to achieve convergence is uniformly bounded independently of the
characteristic size of the underling partition. We also show that the resulting
scheme provides a uniform preconditioner with respect to the number of degrees
of freedom. Numerical results that validate the theory are also presented
Lowest order Virtual Element approximation of magnetostatic problems
We give here a simplified presentation of the lowest order Serendipity
Virtual Element method, and show its use for the numerical solution of linear
magneto-static problems in three dimensions. The method can be applied to very
general decompositions of the computational domain (as is natural for Virtual
Element Methods) and uses as unknowns the (constant) tangential component of
the magnetic field on each edge, and the vertex values of the
Lagrange multiplier (used to enforce the solenoidality of the magnetic
induction ). In this respect the method can be seen
as the natural generalization of the lowest order Edge Finite Element Method
(the so-called "first kind N\'ed\'elec" elements) to polyhedra of almost
arbitrary shape, and as we show on some numerical examples it exhibits very
good accuracy (for being a lowest order element) and excellent robustness with
respect to distortions
An - Primal-Dual Weak Galerkin method for div-curl Systems
This paper presents a new -primal-dual weak Galerkin (PDWG) finite
element method for the div-curl system with the normal boundary condition for
. Two crucial features for the proposed -PDWG finite element scheme
are as follows: (1) it offers an accurate and reliable numerical solution to
the div-curl system under the low -regularity ()
assumption for the exact solution; (2) it offers an effective approximation of
the normal harmonic vector fields on domains with complex topology. An optimal
order error estimate is established in the -norm for the primal variable
where . A series of numerical experiments are
presented to demonstrate the performance of the proposed -PDWG algorithm.Comment: 22 pages, 2 figures, 8 tables. arXiv admin note: text overlap with
arXiv:2101.0346