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Solving Poisson-type equations with Robin boundary conditions on piecewise smooth interfaces. (English) Zbl 1416.65409

Summary: We present two finite volume schemes to solve a class of Poisson-type equations subject to Robin boundary conditions in irregular domains with piecewise smooth boundaries. The first scheme results in a symmetric linear system and produces second-order accurate numerical solutions with first-order accurate gradients in the \(L^\infty\)-norm (for solutions with two bounded derivatives). The second scheme is nonsymmetric but produces second-order accurate numerical solutions as well as second-order accurate gradients in the \(L^\infty\)-norm (for solutions with three bounded derivatives). Numerical examples are given in two and three spatial dimensions.

MSC:

65N08 Finite volume methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations

Software:

PETSc; hypre
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Full Text: DOI

References:

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