Abstract. A numerical method for a two-dimensional curl-curl and grad-div problem is studied in this paper. It is based on a discretization using weakly continuous P1 vector fields and includes two consistency terms involving the jumps of the vector fields across element boundaries. Optimal convergence rates (up to an arbitrary positive ) in both the energy norm and the L2 norm are established ...

Abstract. An interior penalty method for certain two-dimensional curl-curl problems is investigated in this paper. This method computes the divergence-free part of the solution using locally divergence-free discontinuous P1 vector fields on graded meshes. It has optimal order convergence (up to an arbitrarily small ) for the source problem and the eigenproblem. Results of numerical experiments ...

Isometric exercise has been shown to increase metaboliasm in muscle. By contracting agonsit / antagonist muscle pairs, appreciable muscle activity can be achieved. An advanatge of isometric exercise is that no exercise equipment is needed; people can exercise at home on their own. In the present investigation 16 subjects were examined during an isometric co contraction exercise video compared t...

In this work, we investigate the system formed by equations $\text{div } \vec w=g_0$ and $\text{curl w=\vec g$ in bounded star-shaped domains of $\mathbb{R}^3$. A Helmholtz-type decomposition theorem is established based on a general solution above-mentioned div-curl which was previously derived literature. When $g_0\equiv 0$, readily obtain right inverse $\text{curl}$ divergence-free invariant...

In this paper, we present several domain decomposition preconditioners for high-order Spectral Nédélec element discretizations for a Maxwell model problem in H(curl), in particular overlapping Schwarz preconditioners and Balancing Neumann-Neumann preconditioners. For an efficient and fast implementation of these preconditioners, fast matrix-vector products and direct solvers for problems posed ...

This paper considers the problem of vector tomography on an arbitrary bounded domain in three dimensions. The probe transform of a vector eld is the inner product of the Radon transform of a vector eld with a unit vector, called the probe, which may be a function of the projection orientation. Previous work has given reconstruction formulas for arbitrary elds and for those known to be divergenc...