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11	Summation By Parts Finite Difference Methods with Simultaneous Approximation Terms for the Heat Equation with Discontinuous Coefficients Kåhlman, Niklas January 2019 (has links) In this thesis we will investigate how the SBP-SAT finite difference method behave with and without an interface. As model problem, we consider the heat equation with piecewise constant coefficients. The thesis is split in two main parts. In the first part we look at the heat equation in one-dimension, and in the second part we expand the problem to a two-dimensional domain. We show how the SAT-parameters are chosen such that the scheme is dual consistent and stable. Then, we perform numerical experiments, now looking at the static case. In the one-dimensional case we see that the second order SBP-SAT method with an interface converge with an order of two, while the second order SBP-SAT method without an interface converge with an order of one. Finite Difference Method FDM Summation By Parts Simultaneous Approximation Terms SBP-SAT Heat Equation Poisson's Equation Discontinuous Coefficients Piecewise Constant Coefficients Convergence Dual Consistency Stability Computational Mathematics Beräkningsmatematik Discrete Mathematics Diskret matematik Mathematical Analysis Matematisk analys Other Mathematics Annan matematik