We develop and analyze mixed discontinuous Galerkin finite e lem nt methods for the numerical app... more We develop and analyze mixed discontinuous Galerkin finite e lem nt methods for the numerical approximation of incompressible magnetohyd rodynamics problems. Incompressible magnetohydrodynamics is the area of physic s that is concerned with the behaviour of electrically conducting, resistive, incompressible and viscous fluids in the presence of electromagnetic fields. It is modell e by a system of nonlinear partial differential equations, which couples t he Navier-Stokes equations with the Maxwell equations. In the first part of this thesis, we introduce an interior pena lty discontinuous Galerkin method for the numerical approximation of a linear ized incompressible magnetohydrodynamics problem. The fluid unknowns are discr etized with the discontinuousPk-Pk−1 element pair, whereas the magnetic variables are approximated by discontinuous Pk-Pk+1 elements. Under minimal regularity assumptions, we carry out a complete a priori error analysis and pro ve that the energy norm error is o...
ABSTRACT We introduce and analyze a discontinuous Galerkin method for the numerical discretizatio... more ABSTRACT We introduce and analyze a discontinuous Galerkin method for the numerical discretization of a stationary incompressible magnetohydrodynamics model problem. The fluid unknowns are discretized with inf-sup stable discontinuous ℘ k 3−℘ k−1 elements whereas the magnetic part of the equations is approximated by discontinuous ℘ k 3−℘ k+1 elements. We carry out a complete a-priori error analysis of the method and prove that the energy norm error is convergent of order k in the mesh size. These results are verified in a series of numerical experiments.
We develop and analyze mixed discontinuous Galerkin finite e lem nt methods for the numerical app... more We develop and analyze mixed discontinuous Galerkin finite e lem nt methods for the numerical approximation of incompressible magnetohyd rodynamics problems. Incompressible magnetohydrodynamics is the area of physic s that is concerned with the behaviour of electrically conducting, resistive, incompressible and viscous fluids in the presence of electromagnetic fields. It is modell e by a system of nonlinear partial differential equations, which couples t he Navier-Stokes equations with the Maxwell equations. In the first part of this thesis, we introduce an interior pena lty discontinuous Galerkin method for the numerical approximation of a linear ized incompressible magnetohydrodynamics problem. The fluid unknowns are discr etized with the discontinuousPk-Pk−1 element pair, whereas the magnetic variables are approximated by discontinuous Pk-Pk+1 elements. Under minimal regularity assumptions, we carry out a complete a priori error analysis and pro ve that the energy norm error is o...
ABSTRACT We introduce and analyze a discontinuous Galerkin method for the numerical discretizatio... more ABSTRACT We introduce and analyze a discontinuous Galerkin method for the numerical discretization of a stationary incompressible magnetohydrodynamics model problem. The fluid unknowns are discretized with inf-sup stable discontinuous ℘ k 3−℘ k−1 elements whereas the magnetic part of the equations is approximated by discontinuous ℘ k 3−℘ k+1 elements. We carry out a complete a-priori error analysis of the method and prove that the energy norm error is convergent of order k in the mesh size. These results are verified in a series of numerical experiments.
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