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Discontinuous Petrov-Galerkin boundary elements
(2017)
Generalizing the framework of an ultra-weak formulation for a hypersingular integral equation on closed polygons in Heuer and Pinochet (SIAM J Numer Anal: 52(6), 2703-2721, 2014), we study the case of a hypersingular ...
Combining the DPG Method with Finite Elements
(2018)
We propose and analyze a discretization scheme that combines the discontinuous Petrov-Galerkin and finite element methods. The underlying model problem is of general diffusion-advection-reaction type on bounded domains, ...
DPG Method with Optimal Test Functions for a Fractional Advection Diffusion Equation
(2017)
We develop an ultra-weak variational formulation of a fractional advection diffusion problem in one space dimension and prove its well-posedness. Based on this formulation, we define a DPG approximation with optimal test ...
Aspectos computacionais da formulação variacional ultra fraca aplicada ao eletromagnetismo
(Universidade Federal de Minas GeraisUFMG, 2017-03-17)
Numerical methods that use plane waves as basis functions to approximate the solution of the Helmholtz equation have received considerable attention in computational electromagnetics. These approaches do not require the ...
A Time-Stepping DPG Scheme for the Heat Equation
(2017)
We introduce and analyze a discontinuous Petrov-Galerkin method with optimal test functions for the heat equation. The scheme is based on the backward Euler time stepping and uses an ultra-weak variational formulation at ...