Leszek F. Demkowicz

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We give an error analysis of the recently developed DPG method applied to solve the Poisson equation and a convection-diffusion problem. We prove that the method is quasioptimal. Error estimates in terms of both the mesh size h and the polynomial degree p (for various element shapes) can be derived from our results. Results of extensive numerical(More)
The paper presents a description of par3Dhp—a 3D, parallel, fully automatic hp-adaptive finite element code for elliptic and Maxwell problems. The parallel implementation is an extension of the sequential code 3Dhp90, which generates, in a fully automatic mode, optimal hp meshes for various boundary value problems. The system constitutes an infrastructure(More)
I review the main ideas behind the construction of edge elements of variable order 16, 39, 18], and discuss the possibility of extending the construction to Nedelec's elements of the rst kind 31]. A motivation leading to the deenition of hp-interpolation operators is highlighted, and their impact on the hp-discretizations of Maxwell's equations discussed.
New variational formulation to compute propagation constants is proposed. Based on it, vector finite element method is proved to exclude spurious modes provided finite elements possess discrete compactness property. Convergence analysis is conducted in the framework of collectively compact operators. Reported theoretical results apply to a wide class of(More)
The phase error, or the pollution effect in the finite element solution of wave propagation problems, is a well known phenomenon that must be confronted when solving problems in the highfrequency range. This paper presents a new method with no phase errors for one-dimensional (1D) time-harmonic wave propagation problems using new ideas that hold promise for(More)
Discontinuous Petrov Galerkin (DPG) methods are made easily implementable using “broken” test spaces, i.e., spaces of functions with no continuity constraints across mesh element interfaces. Broken spaces derivable from a standard exact sequence of first order (unbroken) Sobolev spaces are of particular interest. A characterization of interface spaces that(More)