Expanded mixed finite element method is introduced to approximate the two-dimensional Sobolev equation. This formulation expands the standard mixed formulation in the sense that three unknown variables are explicitly treated. Existence and uniqueness of the numerical solution are demonstrated. Optimal order error estimates for both the scalar and two vector functions are established.

In-core memory requirement is a bottleneck in solving large three dimensional Navier-Stokes finite element problem formulations using sparse direct solvers. Out-of-core solution strategy is a viable alternative to reduce the in-core memory requirements while solving large scale problems. This study evaluates the performance of various out-of-core sequential solvers based on multifrontal or supe...

We develop an adaptive finite element method for solving the eddy current model with voltage excitations for complicated three dimensional structures. The mathematical model is based on the A−φ formulation whose well-posedness is established. We derive the a posteriori error estimate for the finite element approximation of the model whose solution is not unique in the nonconducting region. Nume...

A finite element solution based on equevalent elements is proposed for the static and dynamic analysis of tallhigh tensioned cable antennas. To reduce high number of degrees of freedom in space frame body of a structure, a simple equivalent beam element is defined for each simulative substructure. This numerical procedure is applicable to analyze complex three dimensional assemblies of substruc...

• Two types of multiscale and monolithic ALE-FEM are developed for the hemodynamic FSI problem that involves aneurysm progression. The heterogeneous method (HMM) seamless (SMM) integrated into ALE-FEM. can predict long-term risk within a short time cardiovascular biological simulations. is numerically validated by 2D example in terms its approximation accuracy. HMM/ALE-FEM applied to AAA patien...

A general formulation for the reduction of the three-dimensional problem of electrothermoelasticity in slender solids to an arbitrarily defined reference line is presented. The dimensional reduction is based on a variationalasymptotic formulation, using the slenderness ratio as small parameter. In the proposed scheme, the coupled linear electroelastic equations are solved at the cross-sectional...

The paper deals with numerical simulation of a compressible flow in timedependent 2D domains with a special interest in medical applications to airflow in the human vocal tract. The mathematical model of this process is described by the compressible Navier-Stokes equations. For the treatment of the time-dependent domain, the arbitrary Lagrangian-Eulerian (ALE) method is used. The discontinuous ...