Numerical solution of parabolic Cauchy problems in planar corner domains

R. Chapko*, B.T. Johansson, V. Vavrychuk

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review


    An iterative method for the parabolic Cauchy problem in planar domains having a finite number of corners is implemented based on boundary integral equations. At each iteration, mixed well-posed problems are solved for the same parabolic operator. The presence of corner points renders singularities of the solutions to these mixed problems, and this is handled with the use of weight functions together with, in the numerical implementation, mesh grading near the corners. The mixed problems are reformulated in terms of boundary integrals obtained via discretization of the time-derivative to obtain an elliptic system of partial differential equations. To numerically solve these integral equations a Nyström method with super-algebraic convergence order is employed. Numerical results are presented showing the feasibility of the proposed approach.

    Original languageEnglish
    Pages (from-to)1-12
    Number of pages12
    JournalMathematics and Computers in Simulation
    Early online date13 Mar 2014
    Publication statusPublished - Jul 2014


    • boundary integral equation
    • Cauchy problem
    • corner singularities
    • heat equation
    • Landweber method


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