We consider numerical solutions of second-order elliptic partial di erential equations, such as Laplace's equation, or linear elasticity, in two-dimensional, non-convex domains by the element-free Galerkin method (EFG). This is a meshless method, in which the shape functions are constructed by using weight functions of compact support. For non-convex domains, two approaches to the determination...

Abstract In this work we analyze the inverse problem of recovering a space-dependent potential coefficient in an elliptic / parabolic from distributed observation. We establish novel (weighted) conditional stability estimates under very mild conditions on data. Then provide error analysis standard reconstruction scheme based output least-squares formulation with Tikhonov regularization (by H 1 ...

In this work we address the analysis of stationary generalized Burgers-Huxley equation (a nonlinear elliptic problem with anomalous advection) and propose conforming, nonconforming discontinuous Galerkin finite element methods for its numerical approximation. The existence, uniqueness regularity weak solutions are discussed in detail using a Faedo-Galerkin approach fixed-point theory, priori er...

A posteriori error estimation for conforming, non-conforming and discontinuous finite element schemes are discussed within a single framework. By dealing with three ostensibly different schemes under the same umbrella, the same common underlying principles at work in each case are highlighted leading to a clearer understanding of the issues involved. The ideas are presented in the context of pi...

Rates of convergence of solutions of various two-dimensional α−regularization models, subject to periodic boundary conditions, toward solutions of the exact Navier-Stokes equations are given in the L-L time-space norm, in terms of the regularization parameter α, when α approaches zero. Furthermore, as a paradigm, error estimates for the Galerkin approximation of the exact two-dimensional Leray-...

Abstract. Accurate modeling of flooding and drying is important in forecasting river floods and near-shore hydrodynamics. We consider the space-time discontinuous Galerkin finite element discretization for shallow water equations with linear approximations of flow field. In which, the means (zeroth order approximation) is used to conserve the mass and momentum, and the slopes (first order appro...

The second order random walk (RW2) model is commonly used for smoothing data and for modelling response functions. It is computationally efficient due to the Markov properties of the joint (intrinsic) Gaussian density. For evenly spaced locations the RW2 model is well established, whereas for irregularly spaced locations there is no well established construction in the literature. By considerin...

We consider a horizontal fluid layer between two rigid boundaries, maintained in a stationary thermal nonequilibrium state below the convective Rayleigh-Bénard instability. We derive an explicit expression for the nonequilibrium structure factor in a first-order Galerkin approximation valid for negative and positive Rayleigh numbers R up to the critical Rayleigh number R(c) associated with the ...