We introduce two robust DPG methods for transient convection-diffusion problems. Once a variational formulation is selected, the choice of test norm critically influences the quality of a particular DPG method. It is ...
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ISBN:
(纸本)9783319416403;9783319416380
We introduce two robust DPG methods for transient convection-diffusion problems. Once a variational formulation is selected, the choice of test norm critically influences the quality of a particular DPG method. It is desirable that a test norm produce convergence of the solution in a norm equivalent to L-2 while producing optimal test functions that can be accurately computed and maintaining good conditioning of the optimal test function solve on highly adaptive meshes. Two such robust norms are introduced and proven to guarantee close to L-2 convergence of the primary solution variable. Numerical experiments demonstrate robust convergence of the two methods.
The goal of this work is the analysis of a time-harmonic eddy current model with prescribed current intensities imposed on the boundary of the conducting domain. We will study a T, phi - phi formulation, which combine...
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ISBN:
(纸本)9783319399294;9783319399270
The goal of this work is the analysis of a time-harmonic eddy current model with prescribed current intensities imposed on the boundary of the conducting domain. We will study a T, phi - phi formulation, which combines a current vector potential T with a scalar potential phi. A significant advantage of this method is that the expensive vector unknown T has to be computed only in conductors. Moreover, the proposed numerical method avoids the building of cutting surfaces what is very convenient in the case of complex geometries.
Evolutionary processes arise in many areas of applied mathematics, however since the solution at any time depends on the solution at previous time steps, these types of problems are inherently difficult to parallelize...
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ISBN:
(纸本)9783319399294;9783319399270
Evolutionary processes arise in many areas of applied mathematics, however since the solution at any time depends on the solution at previous time steps, these types of problems are inherently difficult to parallelize. In this paper, we make a simple proposal of a parallel approach for the solution of evolutionary problems with implicit time step schemes. We derive and demonstrate our approach for both the linear diffusion equation and the convection-diffusion equation. Using an allat- once approach, we solve for all time steps simultaneously using a parallelizable over time preconditioner within a standard iterative method.
The finite element discretization of partial differential equations (PDEs) requires the selection of suitable finite element spaces. While high-order finite elements often lead to solutions of higher accuracy, their a...
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