相关论文: Numerical approximation of the singularly perturbe…
This article presents a unified mathematical framework for modeling coupled poro-viscoelastic and thermo-viscoelastic phenomena, formulated as a system of first-order in time partial differential equations. The model describes the evolution…
In this work, we develop variational formulations of Petrov-Galerkin type for one-dimensional fractional boundary value problems involving either a Riemann-Liouville or Caputo derivative of order $\alpha\in(3/2, 2)$ in the leading term and…
In this study, we derived a three-dimensional scaled boundary finite element formulation for heat conduction problems. By incorporating Wachspress shape functions, a polyhedral scaled boundary finite element method (PSBFEM) was proposed to…
The presence of corners in the computational domain, in general, reduces the regularity of solutions of parabolic problems and diminishes the convergence properties of the finite element approximation introducing a so-called "pollution…
We present a novel hybrid numerical-asymptotic boundary element method for high frequency acoustic and electromagnetic scattering by penetrable (dielectric) convex polygons. Our method is based on a standard reformulation of the associated…
This paper, as the sequel to previous work, develops numerical schemes for fractional diffusion equations on a two-dimensional finite domain with triangular meshes. We adopt the nodal discontinuous Galerkin methods for the full spatial…
This work analyzes a high order hybridizable discontinuous Galerkin (HDG) method for the linear elasticity problem in a domain not necessarily polyhedral. The domain is approximated by a polyhedral computational domain where the HDG…
We introduce an extended discontinuous Galerkin discretization of hyperbolic-parabolic problems on multidimensional semi-infinite domains. Building on previous work on the one-dimensional case, we split the strip-shaped computational domain…
In this work, we propose an easy-to-implement fixed-point algorithm for reconstructing a space-time dependent source in a subdiffusion model from lateral boundary measurements. The numerical scheme combines a Galerkin finite element method…
In this work, we provide a fully-implicit implementation of the time-dependent, filtered spherical harmonics (FPN) equations for non-linear, thermal radiative transfer. We investigate local filtering strategies and analyze the effect of the…
We study the numerical approximation by space-time finite element methods of a multi-physics system coupling hyperbolic elastodynamics with parabolic transport and modeling poro- and thermoelasticity. The equations are rewritten as a…
We present a boundary element method to compute numerical approximations to the non-linear Molodensky problem, which reconstructs the surface of the earth from the gravitational potential and the gravity vector. Our solution procedure…
We begin by addressing the time-domain full-waveform inversion using the adjoint method. Next, we derive the scaled boundary semi-weak form of the scalar wave equation in heterogeneous media through the Galerkin method. Unlike conventional…
In this paper, we consider two-dimensional Riesz space fractional diffusion equations with nonlinear source term on convex domains. Applying Galerkin finite element method in space and backward difference method in time, we present a fully…
Morse and Ingard give a coupled system of time-harmonic equations for the temperature and pressure of an excited gas. These equations form a critical aspect of modeling trace gas sensors. Like other wave propagation problems, the…
We study the existence of solutions to the fractional semilinear heat equation with a singular inhomogeneous term. For this aim, we establish decay estimates of the fractional heat semigroup in several uniformly local Zygumnd spaces.…
This paper presents a hybridized formulation for the weak Galerkin finite element method for the biharmonic equation. The hybridized weak Galerkin scheme is based on the use of a Lagrange multiplier defined on the element boundaries. The…
We describe a numerical method for the solution of acoustic exterior scattering problems based on the time-domain boundary integral representation of the solution. As the spatial discretization of the resulting time-domain boundary integral…
Generalizing the framework of an ultra-weak formulation for a hypersingular integral equation on closed polygons in [N. Heuer, F. Pinochet, arXiv 1309.1697 (to appear in SIAM J. Numer. Anal.)], we study the case of a hypersingular integral…
This paper is devoted to the numerical approximation of a nonlinear temperature balance equation, which describes the heat evolution of a magnetically confined plasma in the edge region of a tokamak. The nonlinearity implies some numerical…