In this article, a posteriori error analysis for mixed finite element Galerkin approximations of second order linear hyperbolic equations is discussed. Based on mixed elliptic reconstructions and an integration tool, which is a variation of Baker’s technique introduced earlier by G. Baker (SIAM J. Numer. Anal., 13 (1976), 564-576) in the context of a priori estimates for a second order wave equ...

We consider a linear, Schrödinger type p.d.e., the ‘Parabolic’ Equation of underwater acoustics, in a layer of water bounded below by a rigid bottom of variable topography. Using a change of depth variable technique we transform the problem into one with horizontal bottom, for which we establish an a priori H estimate and prove an optimal-order error bound in the maximum norm for a Crank-Nicols...

Abstract. We consider the coupling across an interface of fluid and porous media flows with Beavers-JosephSaffman transmission conditions. Under an adequate choice of Lagrange multipliers on the interface we analyze inf-sup conditions and optimal a priori error estimates associated with the continuous and discrete formulations of this Stokes-Darcy system. We allow the meshes of the two regions ...

This paper is the second part of our work on a priori error analysis for finite element discretizations of parabolic optimal control problems. In the first part [18] problems without control constraints were considered. In this paper we derive a priori error estimates for space-time finite element discretizations of parabolic optimal control problems with pointwise inequality constraints on the...

It is still an open problem to prove a priori error estimates for finite volume schemes of higher order MUSCL type, including limiters, on unstructured meshes, which show some improvement compared to first order schemes. In this paper we use these higher order schemes for the discretization of convection dominated elliptic problems in a convex bounded domain Ω in IR2 and we can prove such kind ...

We prove optimal bounds for the discretization error of geodesic finite elements for variational partial differential equations for functions that map into a nonlinear space. For this we first generalize the well-known Céa lemma to nonlinear function spaces. In a second step we prove optimal interpolation error estimates for pointwise interpolation by geodesic finite elements of arbitrary order...

We prove a priori estimates and optimal error estimates for linear finite element approximations of elliptic systems in divergence form with continuous coefficients in Campanato spaces. The proofs rely on discrete analogues of the Campanato inequalities for the solution of the system, which locally measure the decay of the energy. As an application of our results we derive W 1,p–estimates and g...

In this paper, we consider numerical solutions for Riesz space fractional partial differential equations with a second order time derivative. We propose Galerkin finite element scheme both the temporal and spatial discretizations. For proposed scheme, derive sharp stability estimates as well optimal priori error estimates. Extensive experiments are conducted to verify promising features of newl...

Abstract. In this paper, a linearized backward Euler method is discussed for the equations of motion arising in the Oldroyd model of viscoelastic fluids. Some new a priori bounds are obtained for the solution under realistically assumed conditions on the data. Further, the exponential decay properties for the exact as well as the discrete solutions are established. Finally, a priori error estim...