Related papers: Discontinuous collocation and symmetric integratio…
Discontinuous Galerkin (DG) methods for solving elliptic equations are gaining popularity in the computational physics community for their high-order spectral convergence and their potential for parallelization on computing clusters.…
The problem of reconstructing the spatial support of an extended radiating electric current source density in a lossy dielectric medium from transient boundary measurements of the electric fields is studied. A time reversal algorithm is…
Coefficient inverse problems related to identifying the right-hand side of an equation with use of additional information is of interest among inverse problems for partial differential equations. When considering non-stationary problems,…
A $p$-adaptive discontinuous Galerkin time-domain method is developed to obtain high-order solutions to electromagnetic scattering problems. A novel feature of the proposed method is the use of divergence error to drive the $p$-adaptive…
We consider a one-dimensional nonlocal hyperbolic model introduced to describe the formation and movement of self-organizing collectives of animals in homogeneous 1D environments. Previous research has shown that this model exhibits a large…
We study solution techniques for parabolic equations with fractional diffusion and Caputo fractional time derivative, the latter being discretized and analyzed in a general Hilbert space setting. The spatial fractional diffusion is realized…
Computing the rate-distortion function for continuous sources is commonly regarded as a standard continuous optimization problem. When numerically addressing this problem, a typical approach involves discretizing the source space and…
We investigate inverse boundary problems associated with a time-dependent semilinear hyperbolic equation, where both nonlinearity and sources (including initial displacement and initial velocity) are unknown. We establish in several generic…
We propose a variational splitting technique for the generalized-$\alpha$ method to solve hyperbolic partial differential equations. We use tensor-product meshes to develop the splitting method, which has a computational cost that grows…
A linearized numerical scheme is proposed to solve the nonlinear time fractional parabolic problems with time delay. The scheme is based on the standard Galerkin finite element method in the spatial direction, the fractional Crank-Nicolson…
Locally refined meshes impose severe stability constraints on explicit time-stepping methods for the numerical simulation of time dependent wave phenomena. Local time-stepping methods overcome that bottleneck by using smaller time-steps…
The discrete non-commutative Darboux system of equations with self-consistent sources is constructed, utilizing both the vectorial fundamental (binary Darboux) transformation and the method of additional independent variables. Then the…
In this paper, we consider the inverse source problem for the time-fractional diffusion equation, which has been known to be an ill-posed problem. To deal with the ill-posedness of the problem, we propose to transform the problem into a…
The aim of this note is to present a numerical method to solve the Stokes problem in a bounded domain with a Dirac source term, which preserves optimality for any approximation order by the finite-element method. It is based on the…
The paper deals with numerical discretizations of separable nonlinear Hamiltonian systems with additive noise. For such problems, the expected value of the total energy, along the exact solution, drifts linearly with time. We present and…
We present and analyze a discontinuous Galerkin method for the numerical modelling of the non-linear fully-coupled thermo-poroelastic problem. For the spatial discretization, we design a high-order discontinuous Galerkin method on polygonal…
In this work, we consider the numerical solution of an initial boundary value problem for the distributed order time fractional diffusion equation. The model arises in the mathematical modeling of ultra-slow diffusion processes observed in…
Gravitational perturbations in a Kerr black hole background can not be decomposed into simple tensor harmonics in the time domain. Here, we make the mode decomposition only in the azimuthal direction and discuss the resulting…
In this work, we consider space-time goal-oriented a posteriori error estimation for parabolic problems. Temporal and spatial discretizations are based on Galerkin finite elements of continuous and discontinuous type. The main objectives…
In many commercial and academic settings, numerical solvers fail to achieve their theoretical performance levels due to issues in the system definition, parameterization, and even implementation. We propose a pair of methods for detecting…