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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 ...
A robust DPG method for large domains
(2021)
We observe a dramatic lack of robustness of the DPG method when solving problems on large domains and where stability is based on a Poincare-type inequality. We show how robustness can be re-established by using appropriately ...
An Ultraweak Formulation Of The Kirchhoff-Love Plate Bending Model And Dpg Approximation
(2019)
We develop and analyze an ultraweak variational formulation for a variant of the Kirchhoff-Love plate bending model. Based on this formulation, we introduce a discretization of the discontinuous Petrov-Galerkin type with ...
Trace operators of the bi-Laplacian and applications
(OXFORD UNIV PRESS, 2021)
We study several trace operators and spaces that are related to the bi-Laplacian. They are motivated by the development of ultraweak formulations for the bi-Laplace equation with homogeneous Dirichlet condition, but are ...
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, ...