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Studied: Methods of positive coefficients, monotonicity, and the discrete max principle. Stability w.r.t. right hand side, supersolutions, error estimates, convergence, vector vs function norms. Convergence of monotone schemes for hyperbolic transport equations. Von Neumann analysis. Finite element error analysis.

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TMA4212 - Numerisk losning av differensialligninger med differansemetoder

Project 1:

In this project we studied how finite difference methods can be adapted to solve PDE's on irregular domains.

Project 2:

In this project we studied how finite element methods can be used to solve PDE's, and how the error of the numerical solutions behaves.

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Studied: Methods of positive coefficients, monotonicity, and the discrete max principle. Stability w.r.t. right hand side, supersolutions, error estimates, convergence, vector vs function norms. Convergence of monotone schemes for hyperbolic transport equations. Von Neumann analysis. Finite element error analysis.

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