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The time-dependent Ginzburg-Landau equations describing a d-wave superconductor are simulated by the finite-element method. The equilibrium vortex structure in bulk samples, the nature of vortices in bulk and finite-size samples subject to various types of pinnings, and the transport behaviors are addressed. The extended finite-element method proves to be flexible to deal with various types of boundary conditions, desirable to simulate relaxation processes with very long time scales as well asdoi:10.1103/physrevb.54.r15645 pmid:9985723 fatcat:2n2i637szzdmnfnq2zkx4shfje