Related papers: Explicit Time Stepping for the Wave Equation using…
In this article, a numerical analysis of the asymptotic behavior of the discrete energy associated to a dissipative coupled wave system is conducted. The numerical approximation of the system is constructed using the P1 finite element…
This paper discusses lowest-order nonstandard finite element methods for space discretization and explicit and implicit schemes for time discretization of the biharmonic wave equation with clamped boundary conditions. A modified Ritz…
An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves a fractional power of an elliptic operator of second order. Finite element approximation in space is…
Considered here is an efficient technique to compute approximate profiles of solitary wave solutions of fractional Korteweg-de Vries equations. The numerical method is based on a fixed-point iterative algorithm along with extrapolation…
We consider the initial/boundary value problem for the fractional diffusion and diffusion-wave equations involving a Caputo fractional derivative in time. We develop two "simple" fully discrete schemes based on the Galerkin finite element…
We consider an initial-boundary value problem for the $n$-dimensional wave equation with the variable sound speed, $n\geq 1$. We construct three-level implicit in time and compact in space (three-point in each space direction) 4th order…
Source analysis of Electroencephalography (EEG) data requires the computation of the scalp potential induced by current sources in the brain. This so-called EEG forward problem is based on an accurate estimation of the volume conduction…
A numerical procedure providing guaranteed two-sided bounds on the effective coefficients of elliptic partial differential operators is presented. The upper bounds are obtained in a standard manner through the variational formulation of the…
Stability and optimal convergence analysis of a non-uniform implicit-explicit L1 finite element method (IMEX-L1-FEM) is studied for a class of time-fractional linear partial differential/integro-differential equations with non-self-adjoint…
In this paper we focus on high order finite element approximations of the electric field combined with suitable preconditioners, to solve the time-harmonic Maxwell's equations in waveguide configurations.The implementation of high order…
We propose a new discretization method for PDEs on moving domains in the setting of unfitted finite element methods, which is provably higher-order accurate in space and time. In the considered setting, the physical domain that evolves…
We propose and analyze a general framework for space-time finite element methods that is based on least-squares finite element methods for solving a first-order reformulation of the thick parabolic obstacle problem. Discretizations based on…
In this article, we develop a cut finite element method for one-phase Stefan problems, with applications in laser manufacturing. The geometry of the workpiece is represented implicitly via a level set function. Material above the…
Finite element plate and shell formulations are ubiquitous in structural analysis for modeling all kinds of slender structures, both for static and dynamic analyses. The latter are particularly challenging as the high order nature of the…
A space-time domain decomposition approach is presented as a natural extension of the enhanced velocity mixed finite element (EVMFE) [Wheeler et. al] for spatial domain decomposition. The proposed approach allows for different space-time…
Explicit time stepping schemes are popular for linear acoustic and elastic wave propagation due to their simple nature which does not require sophisticated solvers for the inversion of the stiffness matrices. However, explicit schemes are…
We derive a fully computable aposteriori error estimator for a Galerkin finite element solution of the wave equation with explicit leapfrog time-stepping. Our discrete formulation accommodates both time evolving meshes and leapfrog based…
A new field of numerical astrophysics is introduced which addresses the solution of large, multidimensional structural or slowly-evolving problems (rotating stars, interacting binaries, thick advective accretion disks, four dimensional…
An efficient and accurate finite-element algorithm is described for the numerical solution of the incompressible Navier-Stokes (INS) equations. The new algorithm that solves the INS equations in a velocity-pressure reformulation is based on…
A higher-order accurate finite element method is proposed which uses automatically generated meshes based on implicit level-set data for the description of boundaries and interfaces in two and three dimensions. The method is an alternative…