Neela Nataraj

An hp-local discontinuous Galerkin method for some quasilinear elliptic boundary value problems of nonmonotone type

In this paper, an hp-local discontinuous Galerkin method is applied to a class of quasilinear elliptic boundary value problems which are of nonmonotone type. On hp-quasiuniform meshes, using the Brouwer fixed point theorem, it is shown that the discrete problem has a solution, and then using Lipschitz continuity of the discrete solution map, uniqueness is also proved. A priori error estimates in broken H 1 norm and L 2 norm which are optimal in h, suboptimal in p are derived. These results are exactly the same as in the case of linear elliptic boundary value problems. Numerical experiments are provided to illustrate the theoretical results.

A NEW MIXED FINITE ELEMENT METHOD FOR BURGERS' EQUATION

In this paper, anH1-Galerkin mixed finite element method is used to approximate the solution as well as the flux of Burgers’ equation. Error estimates have been derived. The results of the numerical experiment show the efficacy of the mixed method and justifies the theoretical results obtained in the paper.

Analysis of an Interior Penalty Method for Fourth Order Problems on Polygonal Domains

Error analysis for a stable C0 interior penalty method is derived for general fourth order problems on polygonal domains under minimal regularity assumptions on the exact solution. We prove that this method exhibits quasi-optimal order of convergence in the discrete H2, H1 and L2 norms. L∞ norm error estimates are also discussed. Theoretical results are demonstrated by numerical experiments.

An A Posteriori Error Analysis of Mixed Finite Element Galerkin Approximations to Second Order Linear Parabolic Problems

In this article, a posteriori error estimates are derived for mixed finite element Galerkin approximations to second order linear parabolic initial and boundary value problems. Using mixed elliptic reconstructions, a posteriori error estimates in

Improved

L^{\infty}(L^2)

L^2

- and

estimate for gradient schemes and super-convergence of the TPFA finite volume scheme

L^2(L^2)

ON A MIXED-HYBRID FINITE ELEMENT METHOD FOR ANISOTROPIC PLATE BENDING PROBLEMS

-norms for the solution as well as its flux are proved for the semidiscrete scheme. Finally, based on a backward Euler method, a completely discrete scheme is analyzed and a posteriori error bounds are derived, which improves upon earlier results on a posteriori estimates of mixed finite element approximations to parabolic problems. Results of numerical experiments verifying the efficiency of the estimators have also been provided.

Error analysis of nonconforming and mixed FEMs for second-order linear non-selfadjoint and indefinite elliptic problems

The gradient discretisation method is a generic framework that is applicable to a number of schemes for diffusion equations, and provides in particular generic error estimates in

On a two-grid finite element scheme combined with Crank-Nicolson method for the equations of motion arising in the Kelvin-Voigt model

L^2