7 papers · 1 filter
Comparing domain decomposition preconditioners for non-conforming Helmholtz discretizations
Moritz Gallauner, Emile Parolin, Paul Stocker +1
We compare additive and multiplicative domain decomposition preconditioners, without coarse correction, for three non-conforming polynomial discretizations of Helmholtz problems: d…
Embedded Trefftz DG method for steady Navier-Stokes flow. Part I: Oseen linearization
Paul Stocker, Igor Voulis, Christoph Lehrenfeld +1
We develop an embedded Trefftz-DG method for the Oseen problem and prove a complete stability and quasi-optimality theory in standard DG norms. The key ingredient is a construction…
Embedded Trefftz DG method for steady Navier-Stokes flow. Part II: Nonlinear problem
Paul Stocker, Igor Voulis, Christoph Lehrenfeld +1
We develop and analyze an embedded Trefftz-DG method for the steady incompressible Navier-Stokes equations, based on the reduced Oseen discretization from Part I. The main difficul…
Embedded Trefftz DG method for reaction-diffusion problems on anisotropic meshes
Sergio Gómez, Chiara Perinati, Paul Stocker +1
We present and analyze an embedded Trefftz discontinuous Galerkin method for reaction-diffusion problems on anisotropic meshes. The method is constructed by imposing a relaxed loca…
Embedded Trefftz DG method for the Helmholtz equation
Paul Stocker, Igor Voulis
We study an embedded Trefftz discontinuous Galerkin method for the Helmholtz equation. The method starts from a polynomial DG space and enforces the Trefftz property through local…
Adaptive stochastic Galerkin finite element methods: Optimality and non-affine coefficients
Markus Bachmayr, Henrik Eisenmann, Igor Voulis
Near-optimal computational complexity of an adaptive stochastic Galerkin method with independently refined spatial meshes for elliptic partial differential equations is shown. The…