Martijn Anthonissen

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We present a new finite volume scheme for the advection-diffusion-reaction equation. The scheme is second order accurate in the grid size, both for dominant diffusion and dominant advection, and has only a three-point coupling in each spatial direction. Our scheme is based on a new integral representation for the flux of the one-dimensional(More)
We present a finite volume scheme for solving elliptic boundary value problems with solutions that have one or a few small regions with high activity. The scheme results from combining the local defect correction method (LDC), introduced in [13], with standard finite volume discretizations on a global coarse and on local fine uniform grids. The iterative(More)
We apply the finite volume method to a spherically symmetric conservation law of advection-diffusion-reaction type. For the numerical flux we use the so-called complete flux scheme. In this scheme the flux is computed from a local boundary value problem for the complete equation, including the source term. As a result, the numerical flux is the(More)
We study the efficient numerical simulation of laser surface remelting, a process to improve the surface quality of steel components. To this end we use adaptive grids, which are well-suited for problems with moving heat sources. To account for the local high activity due to the heat source, we introduce local uniform grids and couple the solutions on the(More)
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