Article history: Received 14 August 2014 Received in revised form 22 March 2015 Accepted 2 April 2015 Available online 22 April 2015

The solution of elliptic boundary value problems often leads to singularities due to nonsmoothness of the domains on which the problem is posed. This paper studies the performance of the nonconforming hp/spectral element method for elliptic problems on non smooth domains. This paper deals with monotone singularities of type rα and rα log r as well as the oscillating singularities of type rα sin...

In this article, we consider the derivation of hp–optimal spectral bounds for a class of domain decomposition preconditioners based on the Schwarz framework for discontinuous Galerkin finite element approximations of second–order elliptic partial differential equations. In particular, we improve the bounds derived in our earlier article [P.F. Antonietti and P. Houston, J. Sci. Comput., 46(1):12...

We describe the performance of a Spectral Element Atmospheric Model (SEAM) on the HP Exemplar SPP2000. SEAM uses spectral elements in the horizontal directions and sigma coordinates in the vertical. The model is both spectrally accurate, as demonstrated by a variety of test cases, and is well suited for modern distributed-shared memory computers, as demonstrated by the fact that we achieve 24 G...

We present new residual estimates based on Kato’s square root theorem for spectral approximations of non-self-adjoint differential operators of convection–diffusion–reaction type. These estimates are incorporated as part of an hp-adaptive finite element algorithm for practical spectral computations, where it is shown that the resulting a posteriori error estimates are reliable. Provided experim...

We consider the numerical approximation of boundary layer phenomena occur-ing in many singularly perturbed problems in mechanics, such as plate and shell problems. We present guidelines for the eeective resolution of such layers in the context of exisiting, commercial p and hp nite element (FE) version codes. We show that if high order, \spectral" elements are available, then just two elements ...

Finite element simulations have been used to solve various partial differential equations (PDEs) that model physical, chemical, and biological phenomena. The resulting discretized solutions PDEs often do not satisfy requisite physical properties, such as positivity or monotonicity. Such invalid pose both modeling challenges, since the interpretation of simulation results is possible, computatio...