A new two-layer model for impulsive wave generation by deformable granular landslides is developed based upon a discontinuous Galerkin finite element discretisation. Landslide motion modelled using depth-averaged formulation shallow subaerial debris flow, which considers the bed curvature represented local slope angle variable and accounts inter-granular stresses Coulomb friction. Wave propagat...

<p style='text-indent:20px;'>This article presents a conforming discontinuous Galerkin (conforming DG) scheme for second order elliptic equations on rectangular partitions. The new method is based DG finite element space and uses weak gradient arising from local Raviart Thomas approximations. By using the enforcing inter-element continuity strongly, maintains simple formulation of while h...

In this paper, we develop a time and its corresponding spatial discretization scheme, based upon the assumption of a certain weak singularity of IIut(t)llLz(n) = llut112, for the discontinuous Galerkin finite element method for one-dimensional parabolic problems. Optimal convergence rates in both time and spatial variables are obtained. A discussion of automatic time-step control method is also...

In this manuscript we present a p-th degree immersed finite element method for solving boundary value problems with discontinuous coefficients. In this method, interface jump conditions are employed in the finite element basis functions, and the mesh does not have to be aligned with coefficient discontinuity. We show that under h refinement the immersed finite element solution converges to the ...

Discontinuous Galerkin (DG) and matrix-free finite element methods with a novel projective pressure estimation are combined to enable the numerical modeling of magma dynamics in 2D and 3D using the library deal.II . The physical model is an advection-reaction type system consisting of two hyperbolic equations to evolve porosity and soluble mineral abundance and one elliptic equation to recover ...

In this paper we present an a-posteriori error estimator for the mixed formulation of a linear parabolic problem, used for designing an efficient adaptive algorithm. Our space-time discretization consists of lowest order Raviart-Thomas finite element over graded meshes and discontinuous Galerkin method with variable time step. Finally, several examples show that the proposed method is efficient...

This paper deals with a high-order accurate discontinuous finite element method for the numerical solution of the Euler equations. The method combines two key ideas which are at the basis of the finite volume and of the finite element method, the physics of wave propagation being accounted for by means of Riemann problems and accuracy being obtained by means of high-order polynomial approximati...

Starting from the generalized Lax-Milgram theorem and from the fact that the approximation error is minimized when the continuity and inf– sup constants are unity, we develop a theory that provably delivers well-posed approximation methods with unity continuity and inf–sup constants for numerical solution of linear partial differential equations. We demonstrate our single-framework theory on sc...

We consider a standard model for mass transport across an evolving interface. The solution has to satisfy a jump condition across an evolving interface. We present and analyze a finite element discretization method for this mass transport problem. This method is based on a space-time approach in which a discontinuous Galerkin (DG) technique is combined with an extended finite element method (XF...

background : near infrared spectroscopy imaging is one of the new techniques used for investigating structural and functionality of different body tissues. this is done by injecting light into the medium and measuring the photon intensity at the surface of the tissue. method : in this paper the different medical applications, various imaging and simulation techniques of nirs imaging is describe...